Over the course of Roman history, the Senate changed enormously. Do you want to know about the Senate when Rome was ruled (1) by kings (i.e., the regal period), (2) by the senate and people of Rome (i.e., the republic), or (3) by the emperors (i.e., the principate and dominate)?
The period I'm interested in is the time of the Roman republic, when Marius/Sulla/Caeser/Pompey etc were around.