This chapter deals with the basic theory of continuous-time systems. In this chapter, the basic categories of such systems (and, more specifically, causal vs. stochastic/noncausal systems, SISO vs. SIMO vs. MISO vs. MIMO systems, static vs. dynamic systems, linear vs. nonlinear systems, and time-varying vs. time-invariant systems, as well as their combinations) are presented. The concept of stability is analyzed, and the step response, impulse response, and frequency response of continuous-time systems are defined, with an emphasis on these types of responses for linear time-invariant (LTI) systems. Then the focus shifts to the basic forms of system interconnections, namely, connections in series, connections in parallel, and connections with feedback, together with the direct forms I and II and the concepts of reversibility and of inverse systems. The last section of the chapter presents a description of a system in state space. In this section, the concepts of state, state space, and state variables are defined, and the dynamic equations (namely, the state and output equations) in the time domain and in the frequency domain are derived and solved. The section deals also with the fundamental concepts of controllability and observability, as well as stability in state space.