One can either browse the raw list of publications or follow the guidelines below.
The syntax and semantics of the calculus can be found in different papers but a good starting point is the "Rewriting Calculus with Fixpoints" [CLW03] that presents not only the untyped calculus but also a first-order type system suitable for programming purposes. Different operational semantics for this calculus can be found in the overview paper "Rewriting calculus with(out) types" [CKL02].
Several extensions have been proposed for the rho-calculus: a versions handling explicitly the (application of) constraints [CFK04] and [CFK05], a (typed) imperative version of the calculus [LS04] and the corresponding certified interpreter, a version generalizing the patterns from terms to graphs [BBCK04]. The calculus has been also compared to higher-order rewriting and more precisely to CRS [BCK03].
A polymorphic type system can be found in the previously mentioned paper "Rewriting calculus with(out) types" [CKL02] and type checking and type inference issues have been studied in [LW04]. The approach is extended to "Pure patterns type systems" (PPTS) [BCKL03] (the syntax used here is slightly different from the classical one), a generalization of Pure type systems for the rho-calculus. It has been shown that "The simply-typed pure pattern type system ensures strong normalization" [Wac04].
The starting point of PPTS comes from "The Rho Cube" [CKL01b]. The syntax and the semantics of the rho-calculus used here are slightly different from the latest version. The same syntax is used for showing the "Matching Power" [CKL01a], that is the way rho-calculus can encode different (object) calculi.
The syntax and semantics used in these two papers can be seen as the simplification of the initial version of "The Rewriting Calculus" [CK01b,CK01c]. These papers present extensively the initial design of the calculus and the transition to the latest version is presented in [CKLW03]. Several papers present the way this initial version can be used for giving a semantics to rewrite based languages [CK98a,CK98b,CK98c] or other formalisms [CK01a,CK00a]. A simple type system [CK00b] has been introduced and an exception mechanism has been studied [FK02].
There are several reports giving more details on the different topics
enumerated above. The PhD thesis of Horatiu Cirstea [Cir00]
presents the initial version of the calculus, the master thesis of
Clara Bertolissi [Ber02] present the relationship with CRS, the
master thesis of Benjamin Wack [Wac02] deals with the typed
aspects of the calculus, the master thesis of Germain
Faure [Fau03] gives more details on the explicit rho-calculus
and its report [Fau01] presents the way exceptions can be
handled in rho-calculus.