Old English bocian "to grant or assign by charter," from book (n.). Meaning "to enter into a book, record" is early 13c. Meaning "to enter for a seat or place, issue (railway) tickets" is from 1841; "to engage a performer as a guest" is from 1872. U.S. student slang meaning "to depart hastily, go fast" is by early 1980s, of uncertain signification. Related: Booked; booking.
also think-tank, 1959 as "research institute" (first reference is to Center for Behavioral Sciences, Palo Alto, Calif.); it had been colloquial for "the brain" since 1905. See think + tank (n.).