The aim of this thesis is to study the qualitative behavior of a specific non-linear Volterra integro-differential equation with finite delays by using Lyapunov's second method. The non-linear Volterra integro-differential equation is: $x'(t)=b(t)x(t-r_1)-\int_{t-r_2}^{t}a(t,s)g(x(s))ds,$ where $r_1$, $r_2$ are positive constants representing 2 finite delays, $t \geq 0$ and $a : \ [0,\infty) \times [-\tau, \infty) \rightarrow \R, \qquad \text{and} \qquad b : \ [0, \infty ) \rightarrow \R$ are two continuous functions. In the first part, we study the qualitative behavior of the constant ...