This article features the beginnings of the first volume of an encyclopaedia dedicated to the discussion of inter-galactic pedagogical matters. There is much to learn about within and before these times of inter-galactic change and so there is much to consider for those interested in, and committed to, thinking the pedagogical. PEDAGOGICA INTERGALACTICA takes up the task of curating speculations on pedagogy in a galactic context. The entries are included for their role in intersecting concerns with and questions about pedagogies and galaxies. This compilation is presented as a work-in-progress. Entries were selected according to their availability at the time of publication, but given the scope of the research, much information will be available with increases in inter-galactic pedagogues and, at the same time, with pedagogical inter-galactic exploration. While each entry can be understood to take up a speculation on the radical, the seemingly impossible, and the typically unimaginable, each entry can also be understood, and questioned, in the sense of an already is, or at least a very likely could-be.