First published in 1958 by Ace as a Paperback
Originally serialized in Fantastic in in 1958. It is part of the Changewar, a series of stories written by Leiber charting the various battles of the Snakes and the Spiders, two sides fighting a war across time. It won a Hugo in 1957. It was performed as a play at the Babcock Theatre in Salt Lake City in 1982.
Rather wonderfully, you can read the book for free over at Project Gutenberg available.
There are plenty of excellent reviews online.
Review at Yellow and Creased
Review at SFF World
Review at Dreaming of Other Worlds
Review at SF Reviews
Review of the audiobook at SFF Audio
Review at Couch to Moon
There is a free Libravox Audiobook available.
The always interesting Neil Gaiman talks about the Big Time over at The Library of America
“The Big Time, few comparable tour de force exist anywhere in literature…being such a virtuoso performance it doesn’t seem to have had any followers. I admit to keeping it in mind while writing my own ‘A Midsummer Tempest’, but cannot claim that that employs the dramatic unities as the former book did. Evidently nobody in our field can match Fritz Leiber here.”
Poul Anderson in ‘The Wizard of Nehwon’
“Originally published in Fantastic magazine form in 1958 (when it won a Hugo award). The so called Snakes and Spiders are opposing factions in a time war, who recruit their troops from various periods of history. This story, reads almost like a play, involves just one tiny piece of action – but a vaster background is richly suggested. Related short stories are collected in ‘The Mind Spider and Other Stories‘ and in an omnibus volume, that contains this novel, called ‘The Change War‘.
The Ultimate Guide to Science Fiction – David Pringle
Contains the following short stories (listed in alphabetical order)
[amazon text=Amazon&template=my favourites&asin=B0085UUF3Y,B0014KH61G,1606644874,0312890788,0441062229]