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Geometry of Lie groups with left-invariant metrics is well known topic that dates back to classical Milnor's classication of 3-dimensional Lie groups with left-invariant, positive definite metric. The case of indefinite left-invariant metric is less known and with many open problems. The left-invariant metric is always considered up to equivalence with respect to the group of automorphisms. One of the striking differences between positive definite and indefinite setting is the result concerning 3-dimensional Heisenberg Lie group H3. There is, up to a homothety, the unique left-invariant positive definite metric on H3. In contrary, it is the result of Rahmani, that there exist three left-invariant Lorentzian metrics on the same group, one of which is flat. This result motivates us to study geometry of all nonequivalent definite and indefinite metrics on general Heisenberg group H2n+1.