In this study, the theory of continuous crystallization from a supersaturated solution is developed, taking the concentration-dependent fines dissolution, product removal, and feed supply rates into account. These rates make it possible to control the operation mode of the crystallizer and obtain the required supersaturation of the solution, the desired crystal-size distribution in the supersaturated liquid, and the necessary crystal removal rate of the product. The steady- and unsteady-state solutions of model equations are found analytically. It is shown that the non-stationary crystal-size distributions approach the stationary distribution with increasing time. The theory developed is the basis for investigating the linear and nonlinear stability of the crystallizer with allowance for the concentration-dependent fines dissolution, product removal and feed supply rates.