What are the properties of an LTI (Linear Time-Invariant) system?

LTI systems have two fundamental properties: Linearity means the system satisfies superposition - if x1->y1 and x2->y2, then ax1+bx2 -> ay1+by2. Time-invariance means behavior does not change over time - if x(t)->y(t), then x(t-t0)->y(t-t0). LTI systems are completely characterized by their impulse response h(t) or frequency response H(jw). Output is the convolution of input with impulse response: y(t) = x(t) * h(t). Most classical signal processing assumes LTI behavior.