Ln spite of the relative simplicity of the structure of Frenkel excitons in molecular crystals some questions concerning the theory of polaritons in such crystals remain controversial-especially those concerning the crossover from the two-dimensional to the three-dimensional case. In the present work a detailed microscopic study of Frenkel exciton-polaritons in crystal slabs of arbitrary thickness is performed for the states with the tangential wave vector k(parallel to)=0. Starting from the microscopic quantum theory we have obtained two basic equations. One of them relates the complex energy of a polariton E to the quantity q, which in the limiting case of bulk crystal comes to the normal component of the wave vector. When the number N of the monolayers in the pile is large, N much greater than 1, this equation is reduced to the dispersion equation of the macroscopic electrodynamics which uses the dielectric function epsilon(omega). The other equation of our microscopic theory has the meaning of Ewald’s extinction rule and for N much greater than 1 is reduced to Maxwell’s boundary conditions. Using the equations obtained we found the complete set of polariton terms for the arbitrary N from N=1 to N-->infinity. We have traced the rise and evolution of two branches of polariton terms with increasing N. Special attention was paid to the study of polariton superradisnce-enormous radiative damping or very short corresponding lifetimes for some states. At small N much less than lambda/a, with lambda being the light wavelength and a the lattice constant, the superradiant linewidth is proportional to N(lambda/a)T-2((0)), where Gamma((0)) is the molecular radiative width. After further increasing the thickness this linewidth is monotonously decreased to zero. We also show that for the macroscopic slabs the radiative broadening may be obtained as a result of taking into account multiple reflections of the polariton from the surfaces of the crystal. illustrative calculations were performed using parameters of the anthracene crystal.