Animal Man (1991, DC Comics)
This book collects issues #1-#9 of the Grant Morrison run.  The first printing from 1991 displayed the DC logo in the top left corner. The back cover included a Rolling Stone review over a 1981 image of a primate that was supplied by PETA (People for the Ethical Treatment of Animals). It is likely an image of one of the ‘Silver Spring monkeys’ from the Institute for Behavioral Research lab in Maryland.
ISBN: 1563890054

Animal Man (1998, DC Comics/Vertigo)
The 2nd printing from around 1998 included a DC Comics/Vertigo logo on the cover. The back cover image is a detail of the front cover image. Along with the Rolling Stone quote, the back cover mentions the book being back in print after a decade.

Animal Man, Books 1-3 (2002-2003, Vertigo)
The first volume was reprinted in 2002, followed by two further volumes that collected all the Grant Morrison issues (#1-#26, and Secret Origins #39). These printings had the Vertigo logo on the cover.
ISBN: 1563890054 (Vol. 1: Animal Man), 1840234601 (Titan Books UK ed.)
ISBN: 156389890X (Vol. 2: Origin of the Species), 1840234695 (Titan Books UK ed.)
ISBN: 156389968X (Vol. 3: Deus Ex Machina), 184023637X (Titan Books UK ed.)

The Animal Man Omnibus (2013, Vertigo)
The hardcover Omnibus collected all of the issues from the three trade paperbacks into one volume.  It was initially printed with the Vertigo logo but reprinted in 2022 on the DC Black Label imprint.
ISBN: 1401238998

Animal Man, Books 4-7 (2013-2015, Vertigo)
Further volumes were released that collected the post-Morrison issues up until the end of Jamie Delano’s run (#27-#79, and Annual #1).
ISBN: 1401238017 (Vol. 4: Born to be Wild)
ISBN: 1401242847 (Vol. 5: The Meaning of Flesh)
ISBN: 1401246796 (Vol. 6: Flesh and Blood)
ISBN: 1401251234 (Vol. 7: Red Plague)

Animal Man, Lootcrate edition (2017, Vertigo)
A book collecting issues #1-#5 available exclusively to subscribers of Lootcrate DX – a service where subscribers are mailed pop culture collectibles each month. This book was part of the “Primal”-themed box distributed in March 2017 and features an introduction by Grant Morrison and new cover artwork by Yanick Paquette and Nathan Fairbairn.
ISBN: 1401276415 (Lootcrate ed.)

30th Anniversary Deluxe editions (2018-2020, DC Comics/Vertigo)
These two oversized, hardcover volumes include all of the Grant Morrison issues (#1-#26, and Secret Origins #39). Book One of the set was later released as a trade paperback in 2020 on the DC Black Label imprint.
ISBN: 1401285473 (Book 1 HC)
ISBN: 1779505507 (Book 2 HC)
ISBN: 1401299083 (Book 1 TPB)

The Last Days of Animal Man (2010, DC Comics)
This volume collects all 6 issues of the miniseries.
ISBN: 140122640X, 1848565755 (Titan Books UK ed.)

Animal Man (2012-2014, DC Comics)
The 2011 series was collected into five trade paperbacks that include issues #0-29, Swamp Thing #12 & #17 (part of the Rotworld crossover), and Annuals #1-2.
ISBN: 1401235077 (Vol. 1: The Hunt), 1781163448 (Titan Books UK ed.)
ISBN: 1401238009 (Vol. 2: Animal vs. Man)
ISBN: 1401242626 (Vol. 3: Rotworld: The Red Kingdom)
ISBN: 1401246443 (Vol. 4: Splinter Species)
ISBN: 1401249949 (Vol. 5: Evolve or Die)

Animal Man by Jeff Lemire Omnibus (2019, DC Comics)
The hardcover Omnibus collected all of the issues from the five trade paperbacks into one volume and added 80+ pages of additional artwork.
ISBN: 140128941X