  In this paper we introduce generalised Markov numbers and extend the
classical Markov theory for the discrete Markov spectrum to the case of
generalised Markov numbers. In particular we show recursive properties for
these numbers and find corresponding values in the Markov spectrum. Further we
construct a counterexample to the generalised Markov uniqueness conjecture. The
proposed generalisation is based on geometry of numbers. It substantively uses
lattice trigonometry and geometric theory of continued numbers.
