Should you be lucky enough to have the time to peruse, there are more than 2,000 paintings here to enjoy for free -- many of them instantly recognizable and among the most treasured works of art anywhere. The museum's low, gray, colonnaded neoclassic facade fills the north side of Trafalgar Square, which has now been redesigned exclusively for pedestrians, as if the whole square is the grand and spacious entrance to the gallery.

The institution was founded in 1824, when George IV and a connoisseur named Sir George Beaumont persuaded a reluctant government to spend £57,000 to acquire part of the philanthropist John Julius Angerstein's collection. These 38 paintings, including works by Raphael, Rembrandt, Titian, and Rubens, were augmented by 16 of Sir George's own and exhibited in Angerstein's Pall Mall residence until 1838, when William Wilkins's building was completed. By the end of the century, enthusiastic directors and generous patrons had turned the National Gallery into one of the world's foremost collections, with works from painters of the Italian Renaissance and earlier, from the Flemish and Dutch masters, the Spanish school, and of course the English tradition, including Hogarth, Gainsborough, Stubbs, and Constable.

The modern extension of the gallery, the Sainsbury Wing, designed by American architect Robert Venturi, houses the early Renaissance collection, and hosts excellent in-depth exhibitions, on themes or individual artists. Following the pedestrianization of Trafalgar Square, and in anticipation of increasing visitors, the main building is being modernized. Architect Sir Jeremy Dixon (who renovated the Royal Opera House), is also reinventing the somber internal courtyard as a bright, modern atrium. In phase two of the renovation, the museum's Victorian central hall is to be modernized.

The gallery is really too overwhelming to absorb in a single viewing. It is wise to plot a route with the aid of a map from the information desk. Worthy of a look are the exhibitions in the Sunley Room and Room 1, where works are organized along a theme, such as Bosch and Breugel, or focus on an artist, such as El Greco. Alternatively you could start at the Micro Gallery, in the Sainsbury Wing, which gives you access to in-depth information on all of the museum's holdings; you can choose your favorites, and print out a free personal tour map.

The following is a list of 10 of the most familiar works, to jog your memory, whet your appetite, and offer a starting point for your own exploration. The first five are in the Sainsbury Wing. In chronological order: (1) Van Eyck (circa 1395-1441), The Arnolfini Portrait. A solemn couple holds hands, the fish-eye mirror behind them mysteriously illuminating what can't be seen from the front view. (2) Uccello (1397-1475), The Battle of San Romano. In a work commissioned by the Medici family, the Florentine commander on a rearing white warhorse leads armored knights into battle against the Sienese. (3) Bellini (circa 1430-1516), The Doge Leonardo Loredan. The artist captured the Venetian doge's beatific expression (and snail-shell "buttons") at the beginning of his 20 years in office. (4) Botticelli (1445-1510), Venus and Mars. Mars sleeps, exhausted by the love goddess, oblivious to the lance wielded by mischievous putti and the buzzing of wasps. (5) Leonardo da Vinci (1452-1519), The Virgin and Child. This haunting black chalk cartoon is partly famous for having been attacked at gunpoint, and it now gets extra protection behind glass and screens. (6) Caravaggio (1573-1610), The Supper at Emmaus. A cinematically lighted, freshly resurrected Christ blesses bread in an astonishingly domestic vision from the master of chiaroscuro. (7) Velázquez (1599-1660), The Toilet of Venus. "The Rokeby Venus," named for its previous home in Yorkshire, has the most famously beautiful back in any gallery. She's the only surviving female nude by Velázquez. (8) Constable (1776-1837), The Hay Wain. Rendered overfamiliar by too many greeting cards, this is the definitive image of golden-age rural England. (9) Turner (1775-1851), The Fighting Téméraire. Most of the collection's other Turners were moved to the Tate Britain; the final voyage of the great French battleship into a livid, hazy sunset stayed here. (10) Seurat (1859-91), Bathers at Asnières. This static summer day's idyll is one of the painter's best-known works.

The collection of Dutch 17th-century paintings is one of the greatest in the world, and pieces by Hals, Hooch, Ruisdel, Hobbema, and Cuyp are shown in renewed natural light and gracious surroundings. If you visit during the school vacations, there are special programs and trails for children that are not to be missed. Neither are the free weekday lunchtime lectures and Ten Minute Talks, which illuminate the story behind a key work of art. Check the information desk, or Web site, for details. COST: Free, charge for special exhibitions. Tube: Charing Cross or Leicester Sq.