The paper presents and describes the MultiModal MultiDimensional (M3D) system, a novel labeling system for manual gestures that accounts for multiple dimensions of gestures, including gesture form, prosodic features, and semantic-pragmatic contributions. The M3D system consists of an open-access package that has been developed in coordination with five different labs working on gesture and its interaction with speech. It includes a set of reliable annotation guidelines, a validated training program (https://m3d.upf.edu/), and two annotated audiovisual corpora that represent over 60 minutes of lecture-style speech. Together, the authors introduce the M3D gesture labeling system as a valuable tool for advancing research in multimodal communication.