  This paper introduces the ring of all real valued Baire one functions,
denoted by $B_1(X)$ and also the ring of all real valued bounded Baire one
functions, denoted by $B_1^*(X)$. Though the resemblance between $C(X)$ and
$B_1(X)$ is the focal theme of this paper, it is observed that unlike $C(X)$
and $C^*(X)$ (real valued bounded continuous functions), $B_1^*(X)$ is a proper
subclass of $B_1(X)$ in almost every non-trivial situation. Introducing
$B_1$-embedding and $B_1^*$-embedding, several analogous results, especially,
an analogue of Urysohn's extension theorem is established.
