Abstract : We have studied the heating of the solar chromosphere and corona, and the propagation of acoustic waves through the transition region between the chromosphere and corona. In order to place an upper limit on the effectiveness of acoustic waves in heating, we have written and tested a computer program to accurately calculate the propagation and dissipation of vertically travelling acoustic waves which includes thermal conduction and radiative transfer. In order to study heating by other possible waves, in particular magneto-acoustic-gravity waves, we have written and are now testing a computer program which approximately includes horizontal motions. In order to study the effects of horizontal inhomogeneities we have started developing a three-dimensional fluid dynamic computer program. We have also studied the propagation of acoustic waves through the solar transition region. We find that waves with velocity amplitudes compatible with observations near the temperature minimum ( + or - 1 km/s) transmit too little flux through the transition region ( 20,000 erg/sq. cm. -s) to heat the corona. (Author)