Spellbook

Spellbooks were used in Diablo I to learn Spells.

Lore
''More valuable than gold to any sorcerer, books may contain clues to quests, spell formulas, or other pieces of knowledge. The time of the Horadrim is considered to be the greatest age of magic, when untold discoveries in the arcane arts were made. These powerful mystics used every ounce of power at their command to preserve humanity. Although the Eastern mage-clans keep watch over vast libraries of magical tomes, it is suspected that a great part of this knowledge was lost when the last of the Horadrim died. There may be lost works beneath the church that could bring some of these ancient magics to light…''

In-game
They could be found in various places in the Labyrinth such as Bookcases, Skeleton Tomes, and Chests. In addition, they could be obtained by killing enemies or purchased from Adria. They teach you spells of whatever the book's title was. For example: A Book of Firebolt teaches you the Firebolt spell. If you happen to find the book again, you can learn the higher leveled version of the spell.

Not all who wish to improve their spells through reading books may have a chance, however. There is a enforced requirement on a hero's Magic attribute. If the hero does not possess that requirement, they are unable to use the spellbook.

The effect of spellbooks for already-learned spells can vary. In some cases it decreases mana requirement, in other cases it improves spell effect.

For each level earned for a spell, the Magic requirement to gain another level increases by 20% until the requirement reaches at least 192 Magic. After that, the next level (and all subsequent levels, if applicable) require a Magic attribute of 255. The only way to get by without such an imposing restriction is to make use of a certain shrine, namely the Enchanted Shrine, and even then is that type of shrine making the hero suffer from a trade-off which may decrease the level of a desired spell and increase the levels of the others, it would be too harsh for the trivial gains.

Here are the all the available spells you can learn:

In other games
In Diablo II and Diablo III, the spell system was replaced by the Skill Trees, eliminating the need for books. Instead of using books, you would have to spend skill points/choose the desired skills and runes from the list on Skill Trees in order to make your spells/skills more effective.