This thesis describes a search for the double beta (ββ) decay of ⁷⁶Ge using anarray of eight high purity, high resolution germanium detectors containing a totalof 3.9 x 10²⁴ ⁷⁶Ge nuclei. There are three modes of ββ decay: neutrinoless (0ѵ)ββdecay, ββ decay with Majoron emission (x⁰ββ decay) and two neutrino (2ѵ)ββdecay. The first two modes violate lepton number conservation, while the third isallowed by the Standard Model. 0ѵββ decay may take place to the ground state ofthe daughter nucleus (0⁺ → 0⁺ transition) or to an excited state of the daughternucleus (0⁺ → 2⁺ transition). The detector was operated for a total time of 2033 h(0.23 y) which translates to 1.30 kg-y. The background at the ββ decay transitionenergy was 0.53 counts keV⁻¹ y⁻¹ (10²³ ⁷⁶Ge nuclei)⁻¹. No evidence for double betadecay of any sort was found and the half life limits are T0ѵ½(0⁺ → 0⁺) >1.2 x 10²³ y, T0ѵ½(0⁺ → 2⁺) > 2 x 10²² y, Tχo½ > 8 x 10²⁰ y, andT2ѵ½ > 2 x 10²⁰ y, all at 90% c.l. The limit for the neutrinoless mode translates to an upper limit of between 16 and1.6 eV on the Majorana mass of the neutrino, depending on the nuclear matrixelement used.
