  Fermionic expressions for all minimal model Virasoro characters $\chi^{p,
p'}_{r, s}$ are stated and proved. Each such expression is a sum of terms of
fundamental fermionic form type. In most cases, all these terms are written
down using certain trees which are constructed for $s$ and $r$ from the
Takahashi lengths and truncated Takahashi lengths associated with the continued
fraction of $p'/p$. In the remaining cases, in addition to such terms, the
fermionic expression for $\chi^{p, p'}_{r, s}$ contains a different character
$\chi^{\hat p, \hat p'}_{\hat r,\hat s}$, and is thus recursive in nature.
  Bosonic-fermionic $q$-series identities for all characters $\chi^{p, p'}_{r,
s}$ result from equating these fermionic expressions with known bosonic
expressions. In the cases for which $p=2r$, $p=3r$, $p'=2s$ or $p'=3s$,
Rogers-Ramanujan type identities result from equating these fermionic
expressions with known product expressions for $\chi^{p, p'}_{r, s}$.
  The fermionic expressions are proved by first obtaining fermionic expressions
for the generating functions $\chi^{p, p'}_{a, b, c}(L)$ of length $L$
Forrester-Baxter paths, using various combinatorial transforms. In the
$L\to\infty$ limit, the fermionic expressions for $\chi^{p, p'}_{r, s}$ emerge
after mapping between the trees that are constructed for $b$ and $r$ from the
Takahashi and truncated Takahashi lengths respectively.
