New observations in optical frequencies of the peculiar optical and radio galaxy M82 reveal a massive system of filaments which extends along the minor axis to a height of 3000 pc above and below the fundamental plane. Emission lines typical of low-excitation gaseous nebulae are present The filaments on both sides of the plane appear to be expanding from the center along the minor axis with velocities ranging up to about 1000 km/sec. The data suggest that an expulsion of matter took place from the central regions of M82 about 1 5 X 106 years ago. The Ha emission flux from the filaments is estimated to be 1.7 x 10-11 erg at the earth's surface, which requires a total emitted power of 2 X 1040 ergs in Ha if the distance modulus of M82 is m - M = 27.5. The ion density in the filaments, estimated from the volume emissivity, is 10 protons , which then requires the mass of the expanding material to be 5.6 X 106 MO as an upper limit An upper limit to the kinetic energy of the moving gas is 2.4 X 101 ergs. The filaments form fragments of loops and appear to outline lines of magnetic force. Parts of the filaments appear to radiate weakly in the continuum, as well as in the emission lines, and this suggests that optical synchrotron radiation may be present Polarization measurements of part of the filamentary structure by Elvius and Hall are consistent with this possibility. The radio-flux data are combined with an estimate of the optical synchrotron flux, and a theoretical power spectrum is computed from the synchrotron theory. A high-frequency cutoff between 2 X 1014 and 2 X 1015 cps is derived. The total synchrotron energy radiated in 1.5 X 106 years is 9 X 10 ergs if the observed power level has been constant over this time interval. The average maguetic-field strength is estimated to be H < 2 X 10 gauss on the basis that the energy stored in the relativistic electron gas has not been replenished in 1 5 X 106 years and is sufficient to produce 9 X 101 ergs of synchrotron radiation. This energy may have been put into the electrons at the time of the explosion. The time for the high-energy optical electrons to lose half their initial energy is longer than 1 5 X 106 years for a field strength of 2 X 10-6 gauss. Furthermore, if H is this small, the kinetic energy of the moving gas is sufficient to have pulled the field out of the plane of M82 when the expulsion of the matter began. Following Woltjer, it is shown that a possible source of the excitation for the low-energy recombination optical spectrum is the synchrotron-radiation field, which extends to frequencies above the Lyman limit, but more accurate measurements of the Ha and the synchrotron flux are needed to establish this possibility.