'The Big Book of Beasts' (given in quotes with 'the' being part of the name, originally Monster Book) is a recurring item in the Dragon Quest series. It is an optional item that keeps track of nearly all the monsters players can encounter in the game the book appears in. It first appeared in Dragon Quest VII.
Obtaining the book is purely optional and not a requirement to beat the game. It is essentially a convenience for the player, showing all monsters (with some exceptions between games) the player has fought while listing other statistics like the amount of EXP awarded and how many of that particular monster the player has defeated and can even show the monsters' battle animations. Defeating a large number of a single kind of monster will usually result in a minor reward for that monsters page, such as showing more of its animations and revealing what items it drops if the player has yet to obtain any from the monster in question.
Absent from the original game; handed to the main character by his/her adopted father in the remakes. Despite obtaining it in Chapter 5, monsters encountered in the previous chapter show up in the book.
Absent from the original, the book can be purchased at the curiosity shop sometime after the first purchase is made for a wagon.
Absent from the original, the book is obtained in a chest in Haggleton after buying the Thief's key (the Super Famicom version of the game had a Scale shield in the chest). As with Dragon Quest V, the book doesn't track bosses.
The first appearance of the book, where it is a reward in the present for winning the guessing game in Orph's animal appreciation festival.
While there is no actual book to speak of, part of the player's record is a list of monsters they have defeated.
The book's function in this game is provided by the Defeated Monster List in the Battle Records menu (available after Stella is encountered).