This thesis consists of two basic parts. The first part contains a survey on the classical linear topological invariants: $\Gamma,\Gamma^{\prime},m, M .$ In the
second part, we present $\beta$ and Zahariuta invariants and applications on spaces $D(\kappa, a), H(\kappa, \gamma,a),E(\lambda,a).$ These concrete K\"othe
spaces and the invariant are investigated by functional analysists led by V. P. Zahariuta. \vspace{1.5cm}

Keywords : Nuclear, Schwartz K\" othe Spaces, Linear