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The degenerate third Painlev\'{e} equation, $u^{\prime \prime} =\frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8\epsilon u^{2} + 2ab) + \frac{b^{2}}{u}$, where $\epsilon,b \in \mathbb{R}$,and $a \in \mathbb{C}$, and the associated tau-function are studied via theIsomonodromy Deformation Method. Connection formulae for asymptotics of thegeneral as $\tau \to \pm 0$ and $\pm i0$ solution and general regular as $\tau\to \pm \infty$ and $\pm i \infty$ solution are obtained.Comment: 40 pages, LaTeX2

Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation: I