We report an analysis of the X-ray spectrum of Capella from 6 to 175 Aobtained with the Low Energy Transmission Grating Spectrometer (LETGS) on board of the X-ray space observatory CHANDRA. Many emission line features appear that can be resolved much better as compared to former instruments (EUVE and ASCA). Coronal electron densities (n e ) and temperatures (T ) of brightly emitting regions are constrained by an analysis of ratios of density- and temperature-sensitive lines of helium-like ions and highly ionized iron atoms. Lines emitted by e.g., O VII & VIII, Mg X-XII, Si XII-XIV, Fe IX, X & XV-XXIII are used to derive T . Line ratios in the helium-like triplets of C V, N VI, O VII, Mg XI, and Si XIII yield T in the range 0.5-10 MK, and n e in the range 109 -1013 cm-3 . The Fe IX/X ratio yields 0.9 MK, while lines from Fe XVIII to XXII give 6-10 MK. Flux ratios of Fe XX-XXII lines indicate for the electron densities an upper limit in the range (2-5) 1012 cm-3 . From line ratios of Fe XVII and Fe XVIII we derive constraints on the optical depth τ of ~1-1.5. An emission measure distribution is derived from Fe line intensities. Results for element abundances (relative to Fe) from a 4-T model are: O and Ne/Fe about solar, N, Mg and Si/Fe ~2 solar. The results for T and n e are described in terms of quasi-static coronal loop models and it is shown that the X-ray emission originates from compact structures much smaller than the stellar radii.