A spellbook being prepared with level 3 spells
The spellbook lists the spells known by a caster, broken down by class and spell level. It is opened by clicking a button under the player's character's portrait or by hitting the key assigned to the spellbook ('b' by default). For casters that must memorize spells daily, the spellbook also includes a panel listing available spell slots to which known spells can be (or have been) assigned. The memorization panel will have the appropriate number of spell slots for each spell level, determined by class level and casting ability modifier. (In addition, there will be no slots for a given spell level if the caster's modified and base casting ability scores are not both at least 10 plus the spell level.)
A spell can be assigned to a spell slot by either dragging its icon to the slot or clicking the arrow that appears when hovering the mouse over the its name. This causes the slot to be considered "used", but will become "readied" once the character rests. Only spells assigned to readied slots can be cast, and casting a spell uses up that slot. (So to cast a spell multiple times, it is necessary to assign it to multiple slots.) The assignment is not forgotten upon the slot being used, though, so a caster who wants to use the same spells each day needs only to rest; it is not necessary to open the spellbook each game day. (Assignments are forgotten though if the slot is lost, which can happen, for example, through a reduction in casting ability or level drain.)