Multi-classing is one way for a character to have more than one class, the other being dual-classing.

Characters receive the starting gold from all their classes combined – not averaged, not the highest, but combined.¹⁾

We don't restrict multi-class options to the examples given in the PHB. Instead, the only restriction is that multiple classes of the same base class can't be taken (e.g. magic-user/illusionist, or ranger/paladin). Of course, all classes must be qualified for normally, and cannot be incompatible due to alignment.

Track fractional HP for multi-class characters. For example, if a 2-class multi-class character rolls a 5 on a hit die, that player should mark “2.5” on the character sheet. When a full HP is earned, it becomes available. Before then, fractional HP have no game effect.