TECHNOLOGY FOCUS - BIOTECHNOLOGY - Preferred Component: One of the selected microbes is a genetically engineered microbe.    TECHNOLOGY FOCUS - CERAMICS AND GLASS - Preferred Material: The reaction chambers are made of a calcium carbonate-containing cementitious material, where the acidity of waste within the digester is controlled by partial neutralization of acid by the calcium carbonate.    TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Method: The temperature of the digester is not controlled. The anaerobic digestion method further includes adding bacteria to the organic waste or feedstock to the digester; adding sugar to the waste or feedstock in the first reaction chamber, or prior to the first reaction chamber; adding ozone to the organic waste or feedstock prior to its introduction into the digester; and collecting any methane and/or other gases evolved during the anaerobic, microbial digestion of organic waste or feedstock. The pH is maintained at 6-8. The organic waste originates from municipal, industrial, agricultural, or domestic sources.The method of (1) comprises introducing the organic waste or feedstock into an inlet of a first reaction chamber of the digester; and applying adequate pressure to the organic waste or feedstock input to the first reaction chamber so that the waste or feedstock traverses the digester, from the inlet of the first reaction chamber to the outlet of the n-th reaction chamber, at a residence time so that the effluent from the n-th reaction chamber has a reduction in total suspended solids as compared to the input organic waste or feedstock. The method of (2) comprises introducing and applying steps of the anaerobic digestion method; and collecting any methane or hydrogen gas evolved during the anaerobic, microbial digestion of the organic waste or feedstock.Preferred Parameter: The residence time is less than or equal to3 days, or less than or equal to48 (preferably less than or equal to12) hours.    TECHNOLOGY FOCUS - MECHANICAL ENGINEERING - Preferred Component: The digester is controlled by a computer. The computer controls the function of one or more of the further components of the digester. The collection tank has a mixer that mixes organic materials. The pH sensor is positioned in fluid communication with the outflow of the reaction chambers. It is positioned in fluid communication with the outflow of the n-th reaction chamber. It is positioned upstream of the first reaction chamber. The chemical feed tank introduces pH adjusting chemicals. The microbe feed tank has one or more selected microbes. The cleaning apparatus has a pressurized water delivery system. It is positioned in fluid connection with a settling chamber. The water delivery system has a spray nozzle. The removing device has a cyclone or series of cyclones, a pump, and a rotating drum screen. The temperature control device is positioned upstream of the reaction chambers. The gas capture chamber is positioned to receive methane. The digester further comprises a routing channel that routes gas to another selected chamber or to a co-generation skid; the settling chamber adapted to receive at least partially digested organic waste or organic intermediate products from the outlet of the n-th reaction chamber, where the settling chamber has an inlet and an outlet; and a collector to collect any methane and/or other gases evolved during the anaerobic, microbial digestion of organic waste or feedstock. The inlet is near the bottom of the settling chamber. The outlet is near the top of the settling chamber. The settling chamber also has a series of baffles that establish a winding path for the flow of digesting waste or feedstock from the inlet to the outlet of the settling chamber to separate liquids, solids, and gases. The co-generation skid has one or more of a moisture separator, an iron sponge filter, an activated carbon filter, a compressor, a methane-fueled engine, a catalytic exhaust oxidizer, an electric generator, and a switch gear to allow operation of the generator in parallel with an electric utility power grid. The insulation material is placed on the outside of the reaction chambers. The digester is positioned within a container to provide insulation. It lacks temperature control. It contains no introduced microorganisms, other than those microorganisms that are present in the input organic waste without amendment by an operator of the digester. It has at least four reaction chambers. The reaction chambers have compartments within a single vessel, connected one to another to promote the serpentine flow of waste or feedstock through the vessel; or separate vessels linked together, with each separate vessel being mixed or unmixed.Preferred Properties: The rotating drum screen has a screen opening of greater than or equal to500 microns in width. The volume of the first reaction chamber is one quarter-one half of the sum of the volumes of the second and third reaction chambers.    TECHNOLOGY FOCUS - METALLURGY - Preferred Material: The reaction chambers are made of stainless steel.    TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The insulation material comprises 2-4 inches of foam insulation covered by aluminum cladding.