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The library was one of the most important institutions in the Hellenistic and Roman city, as evidenced in the writings of ancient authors, and the building remains of libraries found throughout the Greco-Roman world, from Asia Minor to France and from Africa to Northern Greece. Yet, the library remains one of the least easily identifiable building forms and one of the most difficult to reconstruct, because unlike architectural types such as the temple, stoa, or theater, the library exhibits significant variety in design, scale and monumentality and the use of different component elements. In reconstructing libraries, scholars often rely on a prescribed set of assumptions about components and their arrangement that limit our ability to identify libraries and understand their diversity of arrangement. This dissertation proposes shape grammars as an effective computational methodology to identify, understand, and reconstruct ancient libraries of diverse and variant scale, design and monumentality. The work presents a comprehensive documentation of known and identified libraries, reviews the design principles of the architectural form of ancient libraries, and on the basis of this historical analysis proposes a shape grammar for the formal specification of ancient Greek and Roman libraries. The library grammar encodes the design principles of ancient libraries in ninety-one rules that are grouped in two major parts: the first generates the main hall of the library and its interior design, and the second generates the complete layout of the library including additional porticoes, peristyles, exedras, gardens and propylon. The application of the rules generates libraries of diverse scales and monumentality: libraries known in the corpus and as well as hypothetical libraries. The dissertation presents grammatical derivations for the seventeen known and identified libraries. These derivations, depending on the degree of preservation of the building remains of libraries, function as an evaluative tool for the validity of the grammar or for the reconstructions proposed by traditional research. In many cases, they point to different possibilities in the identification of the building remains related to libraries among remains of different phases or remains belonging to neighboring buildings, and suggest variant scenarios of reconstruction that might not stand out using traditional techniques of reconstruction. The metadata of the rules in the grammar and the derivations are used in a frequency analysis that provides a probabilistic model as an effective and systematic guide in identifying, evaluating and predicting the architectural form of libraries: the main hall and the threshold are identified as mandatory architectural components, the niches and focal point as most likely, and the podium with a colonnade as less likely to occur in a library. Less frequently, the library is a whole complex with exedras, a monumental entry and additional rooms that function as auditoria, banquet halls or offices. Moreover, the work presents the derivations of possible libraries and evaluates the rules applied to generate them based on the frequency analysis. In the end, the work concludes whether these buildings are libraries, non-libraries or exceptional libraries. Lastly, this dissertation assesses the opportunities and challenges that emerge in using shape grammars to identify and reconstruct libraries and also the value and impact of using formal computational methods in the systematic exploration of variations in reconstruction of the archaeological record.