Travel down the broad boulevards of New Delhi, laid out early in the 20th century after the British moved the capital of the Raj from Kolkata to New Delhi and created a new administrative city just south of the old city. Sir Edwin Lutyens, a noted British architect, was given the task of designing this new city, which is still known as Lutyens Delhi; though the British are long gone, this area continues to house India’s government. The British were by no means the only conquerors to make New Delhi their capital. It was also the capital of the Mughal Empire for centuries, so it hosts spectacular examples of Mughal architecture, Humayun’s Tomb, a UNESCO World Heritage Site. Your panoramic tour includes a look at the enormous fort where the emperors lived and a visit to Humayun’s Tomb, erected in 1570, the first Mughal garden tomb in India (and a model for the Taj Mahal and Birla House). The old phrase says that “Delhi belongs to the large-hearted,” and no one was larger hearted than Mahatma Gandhi, the founder of modern India, whose memorial, Raj Ghat, is also on the itinerary this morning.

You have some free time after your tour to explore this exciting city on your own—you’ll find goods from all over India in bustling Connaught Place, in case you want to indulge in some shopping, and the National Museum displays 5,000 years of India’s arts and artifacts. You may opt for the optional tour to Qutab Minar and the Jagannath Hindu Temple.

After a day spent taking in the sights of scenic New Delhi, relax this evening over a delicious buffet dinner at the Oberoi.

Arrive this afternoon at the luxurious Oberoi Amarvilas. Relax over lunch there and then check into your room, where you will be delighted to discover that your room—indeed, every room—has a view of the Taj Mahal, your next destination for the day.

It’s easily the most famous building in India, and one of the most famous in the world, with its white domes and minarets floating serenely above the reflecting pools—and you will encounter it just as the setting sun bathes the white marble in a panoply of colors. It’s a monument to a love story between a great ruler, Shah Jahan, and a learned and powerful woman, his third wife, Mumtaz Mahal. After she died giving birth to their 14th child, he gathered some 20,000 craftsmen to build her mausoleum, who endowed it with dazzling translucent marble carvings inlaid with precious and semiprecious stones. Step through the gate and into the symmetrical gardens, and experience one of the most beautiful places on earth.

Awake early in the morning for a return visit to the Taj Mahal, which will take on the rosy pink tints of sunrise as you arrive. The gates open as the sun lifts above the horizon, and you enter the exquisite precincts, which you may explore at your leisure.

You’ll return to your hotel for lunch before you head by motorcoach to the third city in the Golden Triangle, Jaipur. Capital of the state of Rajasthan, strewn with massive palaces, it was founded and carefully planned in the 18th century by Maharaja Jai Singh II (who gave the new city his name), so even the old part of the city is laid out on a grid. The Singh family’s influence is still felt in Jaipur, though all hereditary titles in India were discontinued in 1971.

Check into the romantic Oberoi Rajvilas, a luxurious oasis, and spend the afternoon relaxing at the hotel, enjoying the extensive, bird-filled gardens.

Following your tour of the Amber Palace, you’ll visit another of Jai Singh II’s architectural projects, the Jantar Mantar, a UNESCO World Heritage Site devoted to astronomy. Each of the curious structures, called yantras, in this observatory without telescopes enabled court astronomers to study the heavens, measuring various celestial phenomena—eclipses, the position of stars—or the time of day. Some of these instruments are still used by astrologers to determine which days will be auspicious for weddings or other important events.

Take the afternoon to explore on your own: Shuttles will be available to carry you to and from the hotel to the major shopping district. Jaipur’s bazaars are famous for their traditional Rajasthani crafts—jewelry, pottery, hand-printed textiles and carpets—so go and enjoy the swirl of colors even if you aren’t interested in buying some souvenirs.

You’ve seen them jostling through the busy streets of New Delhi; today’s your chance to try riding in one yourself. Board a trishaw—a pedal-powered three-wheeled rickshaw—for a view of the streets of Kalna as you head to the Rajbari temple complex. The Pratapeshwar Temple, built in 1849, is embellished with exceptional terra-cotta carvings depicting myths and rituals, as well as scenes of everyday life (see if you can spot the girl in typical Victorian dress with a violin among the hundreds of figures). Lalji, the oldest temple in the complex, dates to 1739; the three-storied structure is topped with 25 distinctive pinnacles. Next to it is Krishna Chandra, built in a similar style. Across the street you’ll find the amazing Naba Kailash, two concentric circles of intricately carved temples dedicated to Shiva. The inner circle is made up of 34 white temples symbolizing pure thought; the outer circle contains 74 temples symbolizing the everyday world.

After marveling at these temples, you may opt to walk with your guide through the colorful local market or return to the ship.

Artisans have been making ornamental brass objects— vases, lamps, figurines, platters—in Matiari for more than a century, so it’s no wonder that production is so well-organized and the craftsmen so skillful. Scrap metal is melted in the village foundry and pressed into new sheets of brass, which are then turned into various objects. Each craftsman specializes in a different step of the process, so one artisan might cut the metal, while another shapes it into a wide tray, and yet another etches an intricate pattern onto the surface. The sound of hammer on brass will fill the air as you stroll from workshop to workshop to see each step of the fascinating process.

Back onboard, watch as a skilled practitioner of mehndi demonstrates how the intricate henna patterns are created, and discover the meanings of the traditional motifs.

Your day begins in Murshidabad, long ago the capital of Bengal and an important administrative center during the Raj—a fact that comes clear as the ship rounds a bend in the river and you behold Hazarduari Palace. This massive neoclassical building was erected in the mid-19th century for British officials, who lived and had their offices in its 114 rooms. One might wonder why the architect, Colonel Duncan Macleod of the Bengal Corps, thought the building needed a thousand doors, but that’s how many it has—900 of them are real doors, and the remaining 100 are false. It is now a museum, which you will visit. Climb aboard a horse-drawn buggy for a ride to Katra Mosque, built in 1723 by the first nawab, Murshid Quli Khan, who gave his name to the town. The huge mosque was damaged by an earthquake in 1897, losing two of its four great towers, but it is still a remarkable sight.

Return to the ship for lunch and cruise to the town of Baranagar, where Rani Bhabani built beautiful brick temples in the 18th century. Goats frolic among them now and vines attempt to take them over, but the terra-cotta carvings are considered among the best in Bengal and the temples are well-tended.

After your tour, if time and weather allow, you can learn a bit about one of the Raj’s enduring legacies in India: a passion for that most British of all games, cricket. It remains India’s favorite sport, and the national team, nicknamed the “Men in Blue,” has won the Cricket World Cup more than once. The game is played in schools, in fields, even on village streets; watch it in action and discover the meaning of terms like “long leg,” “fast bowler” and “run-out.”

As the ship comes into sight of Mayapur, look for the new Vedic temple currently under construction. Funded in part by Alfred Ford, great-grandson of Henry Ford, the temple is designed to be larger than St. Paul’s Cathedral in London once completed. The new temple construction coincides with the 50th anniversary of the founding of the Hare Krishna movement, whose founder was born in Mayapur. Millions of Hare Krishna devotees come from all over the world to this pilgrimage site; as you walk through Mayapur’s bazaar to the temple complex, you may well spot expatriates from America, Canada and Europe. Colorful parades of followers often weave through the streets, adding to the hustle and bustle of the lively, vivid scene. You’ll tour the existing temple complex, get a look at the new Vedic Planetarium and learn something about the beliefs of the International Society of Krishna Consciousness.

Bandel, founded by Portuguese traders in the 16th century, offers a typically Indian mix of religious monuments: It’s the site of the oldest Christian church in India, the location of Hindu festivals (including one devoted to the goddess Muthumariamman), and home to a famous Shia pilgrimage center, the Hooghly Imambara. You’ll board a country boat—a small boat fitted with benches that ferries passengers to and from your luxurious ship, which cannot always moor on the banks of the river—to reach the shore and the imambara. Completed in 1861 to honor Muhammad Mohsin, a revered Bengali philanthropist, the stately imambara offers shelter for pilgrims, a mosque and a school. Step into the long colonnaded courtyard for a view of the twin towers and the 19th-century clock, and climb the stairs of the clock tower for a fabulous view of the river and surrounding countryside. Visitors are sometimes allowed into the mosque, but all guests must leave before the faithful are called to evening prayers.

“Liberté, Egalité et Fraternité.” These words, the famous slogan of the French Revolution, are inscribed on the gateposts of Chandannagar, a memento of the centuries the town was a French outpost in West Bengal. In fact, Chandannagar did not officially become part of India until 1952, so when you step ashore here you will find a mixture of French Colonial and Indian architecture. A broad, tree-lined riverfront promenade known as the Strand shows off the handsomest remaining French buildings, including the Dupleix Palace, now a museum, and the 19th-century Church of the Sacred Heart that replaced the 17th-century original.

Continue this morning with a panoramic tour of Kolkata’s city center. The first stop? A visit to the captivatingly colorful Flower Market. Located adjacent to the Howrah Bridge, this vibrant and bustling market is filled with vendors and buyers exchanging money for flowers to be used in festivals, rituals, weddings and more. You’ll also have the chance to witness local wrestlers practicing early in the morning in an area along the riverbank. Though teeming Kolkata is home to palaces and tenements, new developments and modern office buildings, grand hotels and parks, its historic architecture reflects its status as the longtime administrative heart of the British Raj. The colonial buildings still standing—and still in use—offer a blend of baroque and neoclassical styles that say much about British colonial taste. Perhaps the most surprising is the red-and-white façade of the Calcutta High Court building—a replica of the city hall in Ypres, Belgium. You’ll see it as well as the stately Palladian dome of Government House, the classical white columns of Town Hall, the red-brick Writers’ Building and the enormous General Post Office. Pay a visit to St. John’s, the oldest Anglican church in the city, and the Victoria Memorial Museum—which was partly inspired by the Taj Mahal. Built as a tribute to Queen Victoria after her death, this huge white-marble structure houses an illuminating exhibition on the colonial era. From there, you’ll venture to Kumartulli, a traditional potters’ neighborhood that specializes in making intricate clay idols, for a look at this complex and fascinating time-honored tradition.

This afternoon, you’ll visit the local NGO Kolkata Rescue, which serves the area’s underprivileged children. They provide much-needed services at no cost to the neediest people of Kolkata and West Bengal—regardless of gender, age, caste or religion—through health clinics, schools, vocational training and preventative health programs. You’ll hear about the impact Kolkata Rescue has made over the last 30 years and get some insight on some of their current projects.

She came to India in 1929, after growing up in Macedonia and joining a Loreto nunnery in Ireland, and two decades later she founded her own order, the Missionaries of Charity, devoted to the “salvation and sanctification of the poorest of the poor.” Visit the Mother House, where she lived and worked for decades; see her simply furnished room and the tiny museum devoted to her—her Nobel Peace Prize medal is on display, along with informative newspaper clippings and photos—and her tomb. It’s a modest and serene spot devoted to one of the most influential women ever to live in the city.