SANTA MONICA, Calif., Oct. 15--Cole Porter, the world-famed composer and lyricist, died at 11:05 P.M. today at a Santa Monica hospital, where he underwent kidney surgery last Tuesday. He was 72 years old. Mr. Porter wrote the lyrics and music for his songs, and to both he brought such an individuality of style that a genre known as "the Cole Porter song" became recognized. The hallmarks of a typical Porter song were lyrics that were urbane or witty and a melody with a sinuous, brooding quality. Some of his best-known songs in this vein were "What Is This Thing Called Love," "Night and Day," "Love for Sale" and "Begin the Beguine." But an equally typical and equally recognizable Porter song would have a simple, bouncy melody and a lyric based on a long and entertaining list of similarities, opposite or contrasts. "Let's Do It" ticked off the amiable amatory habits of birds, flowers, crustacea, fish, insects, animals and various types of humans, while "You're the Top" was an exercise in the creation of superlatives that included such items as "the nimble tread of the feet of Fred Astaire," "Garbo's salary" and "Mickey Mouse." Still a third type of Porter song was exclamatory in both lyrics and melody. "Just One of Those Things," "From This Moment On" and "It's All Right With Me" were instances. The glossy opulence of the scores Mr. Porter wrote for Broadway and Hollywood was a valid reflection of his own manner of living. Between World Wars he and his wife, the former Linda Lee of Louisville, Ky., were active in a gay international set that gathered at Paris, the Riviera and Venice. Their home on the Left Bank in Paris had platinum wallpaper and chairs upholstered in zebra skin. Mr. Porter once hired the entire Monte Carlo Ballet to entertain his house guests. For a party in Venice, where he rented the Palazzo Rezzonico for $4,000 a month, he hired 50 gondoliers to act as footmen and had a troupe of high-rope walkers perform in a blaze of lights. Most of Mr. Porter's songs were written far from Broadway. His score for "Anything Goes," which included "I Get a Kick Out of You," "You're the Top," "All Through the Night" and the title song, was composed while he was cruising down the Rhine. He wrote the songs for "Jubilee" ("Begin the Beguine," "Just One of Those Things" and "Why Shouldn't I?" among others) during a round-the- world cruise with the show's librettist, Moss Hart. But Mr. Porter was no dilettante composer. Not even the rigors of his busy social rounds interfered with his creativity. "I've done lots of work at dinner, sitting between two bores," he once said. "I can feign listening beautifully. I can work anywhere." He was a careful craftsman whose work won the admiration of his peers. Richard Rodgers has said, "Few people realize how architecturally excellent his music is. There's a foundation, a structure and an embellishment. Then you add the emotion he's put in and the result is Cole Porter." Mr. Porter himself could not characterize his songs. "I don't know how my music gets that way," he said when he was asked to make the effort. "I simply can't analyze it. I can analyze the music of others. The word for Dick Rodgers's melodies, I think, is holy. For Jerome Kern, sentimental. For Irving Berlin, simplicity. For my own, I don't know." Mr. Porter was a trim, slight, dark man, groomed in subdued, elegant taste. He usually sported a boutonniere in the lapel of his well-tailored suits. His speech was quiet, reserved, almost clipped. He was born on a 750-acre farm in Peru, Ind., on June 9, 1892, the son of Samuel Fenwick Porter, a fruit grower, and the former Kate Cole. He could play the violin when he was 6 and the piano when he was 8. At the age of 10 he composed a song, "The Bobolink Waltz," that pleased his mother so much that she had it published in Chicago. Despite the boy's musical leanings, his maternal grandfather, J. O. Cole, who had made a fortune in the lumber business, wanted him to be a lawyer. To this ostensible end, young Porter was sent to Worcester Academy in Massachusetts and to Yale, where he wrote two of the most famous of all college songs, "Bingo Eli Yale" and the "Yale Bulldog Song." He continued his studies at the Harvard Law School but, at the suggestion of the dean, transferred to the School of Music. With a fellow student, T. Lawrason Riggs, he wrote a show, "See America First," which was produced on Broadway in 1916 with a cast that included Clifton Webb. It was a failure. Mr. Porter then joined the French Foreign Legion where he had a specially constructed portable piano made for him so that he could carry it on his back and entertain the troops in their bivouacs. In 1919 he married Mrs. Linda Lee Thomas, widow of E. R. Thomas, a banker and publisher, and settled in Paris. Mr. Porter made casual contributions to two revues during the early 1920's, "Hitchy-Koo" and "Greenwich Village Follies of 1924," but he was not induced to write a Broadway score again until 1928, where he contributed the songs to "Paris," a play with incidental music that starred Irene Bordoni. Only five of Mr. Porter's songs were used in the final production, but one was the provocatively amusing "Let's Do It." During the intervening years he had been writing and performing songs for the amusement of his friends, but the reception accorded "Let's Do It" apparently convinced him that he could communicate pleasurably to a broader audience. As a result, a steady series of Porter show scores and a wide variety of memorable songs followed during the next 15 years. Among these shows and songs were "Fifty Million Frenchmen" in 1929 ("You Do Something To Me"); "Wake Up and Dream," also 1929 ("What Is This Thing Called Love"); "The New Yorkers" in 1930 ("Love for Sale"); "Gay Divorce" in 1932 with Fred Astaire ("Night and Day"); "Anything Goes" with Ethel Merman, Victor Moore and William Gaxton in 1934 ("You're the Top," "I Get a Kick Out of You"); "Jubilee" in 1935 ("Begin the Beguine," "Just One of Those Things"); "Red, Hot and Blue" with Miss Merman, Jimmy Durante and Bob Hope in 1936 ("It's De-lovely," "Down in the Depths of the '0th Floor"). Also, "Leave It to Me" in 1938 in which Mary Martin made her Broadway debut singing "My Heart Belongs to Daddy"; "Dubarry Was a Lady" with Miss Merman and Bert Lahr in 1939 ("Friendship"); "Panama Hattie" with Miss Merman in 1940 ("Make It Another Old Fashioned, Please"), "Let's Face It" in which Danny Kaye sang "Melody in 4F" in 1941; "Something for the Boys" with Miss Merman in 1943 and "Mexican Hayride" with Bobby Clark in 1944. While Mr. Porter was horseback riding in the summer of 1937, his horse slipped, threw him and fell on top of him, breaking both his legs and damaging his nervous system. One result of Mr. Porter's accident was chronic osteomyelitis, a bone disease. In attempts to alleviate this, he was subjected to more than 30 operations during the next 20 years but, despite this, his right leg had to be amputated in 1958. For the rest of his life, Mr. Porter lived under the constant pressure of pain and, reversing his previously gay social life, became a virtual recluse. Still he continued to turn out his songs. The score for "Leave It to Me," written shortly after his accident, was composed while he was almost completely bedridden. In order to continue his work, he had his piano placed on blocks so that he could roll up to the keyboard in his wheel chair. At the end of World War II, Mr. Porter hit what seemed to be a dry period. Two successive shows-- "Seven Lively Arts" in 1944 and "Around the World in 80 Days" in 1946--were failures. But in 1948 he came back with his biggest artistic and commercial success, "Kiss Me Kate," a musical treatment of "The Taming of the Shrew." In this score, Mr. Porter was not only at his Porterian best with such songs as "Too Darn Hot," "Always True to You in My Fashion" and "So in Love," but he also revealed a remarkable talent for blending the idioms of both Porter and Shakespeare in "I've Come to Wive It Wealthily in Padua," "I Am Ashamed that Women Are So Simple," "I Hate Men" (which Brooks Atkinson called "the perfect musical sublimation of Shakespeare's evil-tempered Kate") and the kind of grammatical challenge that Mr. Porter relished, a song written entirely in the subjunctive, "Were Thine That Special Face." Mr. Porter's later Broadway scores included "Out of This World" (1950), "Can-Can" (1953) and "Silk Stockings" (1955). For films he wrote "I've Got You Under My Skin" and "Easy to Love" for "Born to Dance" in 1936; "Rosalie" and "In the Still of the Night" for "Rosalie" in 1937; "I Concentrate on You" for "Broadway Melody" in 1940 and "You'd Be So Nice to Come Home To" for "Something to Shout About" in 1943. Mr. Porter's wife died in 1954. During his last years he lived in a nine-room, memorabilia-filled apartment in the Waldorf Towers. On weekends he was driven to a 350-acre estate in the Berkshires and in the summers he lived in California. He rarely saw anyone except intimate friends. A 90-minute television program honoring him was presented in 1960, and a party celebrating his 70th birthday was given in 1962, but he was unwilling to attend either event. When Yale University wished to confer an honorary degree of Doctor of Humane Letters on him in 1960, Mr. Porter accepted on condition that the presentation be made in his apartment.