Terry Gilliam began as a cartoonist but came to prominence creating animations for television, first for the children's series Do Not Adjust Your Set (1967-69) and subsequently for Monty Python's Flying Circus (1969-74). His surreal cut-out style gave the television program an unique appeal. As the comedy troupe extended into film, Gilliam became an accomplished director, now having 14 feature films to his credit. These include Time Bandits (1981), Brazil (1985), The Fisher King (1991) and 12 Monkeys (1995).
From the video post:
"Storytime" is a short animated comedy film written, directed and animated by Terry Gilliam. It is Gilliam's first film, and stylistically anticipates the distinctive animations which Gilliam went on to produce for Monty Python's Flying Circus. "Storytime" is composed of three loosely connected animated segments. The first two, "Don the Cockroach" and "The Albert Einstein Story", were originally broadcast in the 1971–1972 TV series The Marty Feldman Comedy Machine, while the third, "The Christmas Card", was created for the 1968 Christmas Special of Do Not Adjust Your Set. It is not clear when the three segments were first compiled to create "Storytime", but the film was eventually included on the Jabberwocky DVD as a bonus feature. It was also shown as an accompaniment to some British theatrical releases of Monty Python's Life of Brian.
Here's a documentary where Gilliam demonstrates his method.