Solid state physics can be viewed from either a deeply theoretical or a more engineering-oriented point of view. For physicists, solid state physics offers a chance to apply and test quantum mechanical and themodynamical principles. Solid state is one of the core subfields in physics, and is perhaps the one with the most applications. From a physicist's perspective, solid state physics is the study of crystals, and that node might be a good starting point for further exploration.
While heady, quantum mechanics-based solid state physics has practical applications, it is often unsuitable for engineering purposes. An electrical engineer uses solids to build circuits, make semiconductor lasers, produce optical fibers, etc. Engineers working on a 100-million transistor circuit have many purely engineering-type things to worry about. For their purposes, condensed, nonrigorous, easily-applied theory is necessary. There are many books with titles like semiconductor physics (generally they include information on other materials too) that offer this sort of theory. These books are not necessarily easy reading, but they focus on important topics such as simple bandstructure models, carrier statistics, carrier transport, and semiconductor devices.
From an engineer's point of view, metals and dielectrics are usually easier to deal with than semiconductors. Metals are just wires. Dielectrics are just insulators. Semiconductors can do many exciting and useful things (like run your computer). Therefore it is not a terrible lack of generality to refer to the engineering version of solid state physics as semiconductor physics, a node I just created.
A wonderful physics-oriented reference: Solid state physics by Ashcroft/Mermin
A popular engineering-oriented reference: Semiconductor Devices by Robert Pierret
A more far-reaching engineering-type reference: Semiconductor Devices by Jasprit Singh