Basic Electronics
Study of basic electronic principles should not be skipped. The better you intuitively understand electronics, the easier troubleshooting will be.
Components
Passive Linear Components
Resistor
Capacitor
Inductor
Passive Non-Linear Components
Diode
Varistor
Active Components
Transistor
Integrated Circuit
Circuits
Using Node Analysis as a Troubleshooting Tool
Troubleshooting often involves writing down the dc and ac conditions with respect to some common node on the schematic (usually called "ground"). This is a powerful way to logically find the fault in the circuit without soldering. Writing down the voltages is only halfway there though. You must be able to calculate what the voltages should be with working devices, and you must know your theory well in order to do this.
Suggesting reading to aid in learning node analysis:
Norton's Theorem
Superposition Theorem