"In the first part of the talk, we introduce the concept: Controllability of Differential Equations. Then we give some examples in finite (ODE) and infinite dimensional(PDE) contexts. We recall the controllability results of the Transport and Heat equation. In the second part of the talk, we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state (Q_0, V_0 ) , with Q_ 0 > 0, V 0 >0 . It is a Coupled system of transport and heat type equations. We study the boundary null-controllability of this linearized system in the interval $(0,1)$ when a Dirichlet control function is acting either only on the density or only on the velocity component at one end of the interval. We obtain null controllability using one boundary control in the space ${H}^s_{per}(0,1)times L^2(0,1)$ for any $s>frac{1}{2}$ provided the time $T>1$, where ${H}_{per}^s(0,1)$ denotes the Sobolev space of periodic functions. The proof is based on a spectral analysis and on solving a mixed parabolic-hyperbolic moments problem and a parabolic-hyperbolic joint Ingham-type inequality. This is a recent joint work (https://arxiv.org/abs/2204.02375, 2022) with Kuntal Bhandari, Rajib Dutta and Jiten Kumbhakar. "