A fine museum that opened as part of the royal art school in 1843 houses works spanning some 550 years. Among many early masterpieces is Hans Memlings’s “Bathsheba at Her Bath” (from around 1440), a brilliant piece of portraiture in which the artist captures beads of moisture on his subject’s brow and her long hair twisted into a knot; bathing Bathsheba, believed to represent the cleansing act of baptism, provided artists with a church-sanctioned means to paint the naked female body. Your reflections on this work and those by other old masters, who were revolutionary in their time, might enhance your appreciation of the adjoining New State Gallery, a controversial addition with an undulating façade designed by the British architect James Stirling and completed in 1984. Galleries surrounding a glass rotunda house a collection of 19th- and 20th-century works that has made the museum into a noted repository of modern art. Picasso’s “Inclined Head of a Woman” and Matisse’s “La Coiffeur” are among many works from the early 20th century, with Mondrian, Gris, Braque, and many other European artists of the time well represented. Curators worked throughout the latter part of the century to reconstitute collections lost to World War II and Nazi purges, with admirable results: Max Beckmann’s “Self Portrait with Red Scarf” is one of relatively few early works of the artist to survive, and the museum has also brought together a sizable number of other works by the Bauhaus school and Blue Rider group, much vilified by the National Socialists.