Applying the linearized equations of motion, projection on the complex plane and a representation of the velocity vector and the forcing sea surface elevation gradient in function of the eigenvectors of the homogeneous system, we developed a theory that explains essential properties of tidal currents. We found the existence of a fundamental vector which we call sense of rotation s. The ellipticity, until now defined as a scalar quantity, results from the theory as a vector $varepsilon$ , normalized from s. $varepsilon$ is a measure of the eccentricity and sense of rotation of tidal ellipses and has some properties that are similar to those of the angular velocity. We derived an expression for the major and minor semi-axis in function of physical properties and characteristics of amphidromic systems. These and other results of the theory allow the analysis of important aspects of tidal currents.