Maxwell's equations are analytically solved in time domain for one-dim
ensional plane TEM-waves in lossy, homogeneous and linear media with R
iemann's method. The calculated closed form fundamental solutions for
both electric and magnetic fields are formulated for arbitrary wave sh
apes, up to impulse waves, which is one advantage over the well known
frequency domain solutions. In addition to this they give more insight
to the physical understanding of wave propagation in lossy media. The
se fundamental solutions are very well suited to examine the reflectio
n and transmission properties of layered lossy media in time domain, b
ecause they are solutions of a characteristic initial Value problem.