Short answers, pulled from the story.
Lewis Carroll was the pen name of Charles Lutwidge Dodgson (the 27th of January 1832 - the 14th of January 1898), an English author, poet, mathematician, photographer, and Anglican deacon. The pseudonym was derived by translating his real name into Latin and back into English, then reversing the result, and was first used in print in March 1856.
On the 4th of July 1862, Dodgson invented the outline of the story during a rowing trip to Godstow with Alice Liddell and her sisters. Alice Liddell begged him to write it down, and he eventually presented her with a handwritten illustrated manuscript titled Alice's Adventures Under Ground in November 1864. It was published in expanded form as Alice's Adventures in Wonderland in 1865 with illustrations by Sir John Tenniel.
Dodgson worked in geometry, linear and matrix algebra, mathematical logic, and recreational mathematics. He introduced the Method of Trees in Symbolic Logic Part II, recognised as the earliest modern use of a truth tree. His work on Dodgson condensation, a method of evaluating determinants, later led researchers to the alternating sign matrix conjecture, now a theorem.
Lewis Carroll invented the word ladder puzzle, which he called "Doublets": the goal is to transform one word into another by changing one letter at a time, with each step producing a genuine word. It first appeared in Vanity Fair on the 29th of March 1879, and Carroll wrote a weekly column for the magazine for two years, with the final column dated the 9th of April 1881.
Dodgson spent almost his entire adult life at Christ Church, a constituent college of the University of Oxford. He went into residence in January 1851, won the Christ Church Mathematical Lectureship in 1855, held it for 26 years, and remained in residence at Christ Church until his death in 1898.
Dodgson died of pneumonia following influenza on the 14th of January 1898, less than two weeks before his 66th birthday, at his sisters' home "The Chestnuts" in Guildford, Surrey. His funeral was held at St Mary's Church, and he was interred at the Mount Cemetery in Guildford.