Analog electronics is the study of electronic circuits which manipulate analog signals. This branch of electronics not only applies to devices purely in itself for analog signal processing, but also serves a vital, complementary role to digital electronic systems, in the field of mixed signal circuits. See the difference between analog and digital circuits w:Analog_circuits#Analogue_vs._digital_electronics
Analog systems deal with electrical quantities (of voltage and current) which vary continuously over a range. In this approach, they are fundamentally different from digital systems, which have to group ranges of these quantities together to be understood.