Battle magic is an ancient Imperial fighting tradition, and can be learned like any other, though the places that teach it nowadays are either prohibitively expensive or only accept the most talented, and wild talents are rare at best and nearly unheard of in official service (if only because the organized academies want to squash the idea of that before it starts to take root). Traditional magic includes Biokinesis, Laying on Hands, Numbing Touch, Psychokinesis, and Telekinesis.
Some more subtle magic exists but isn’t well known – either because of the toll on the user or because people who learn it tend to attract unwanted attention. This includes Aura Reading, Automatic Writing, Clairvoyance, Medium, Omen Sensitivity, and Psychometry. These usually require research to learn and shouldn’t be bought without such an effort.
Some magic has been hoarded by certain factions – specifically, the Ecclesium and Legio Arcanum both have secrets locked away. Access to this requires Status * in the respective faction and being trusted enough that they will train you in specific use.
Some magic is forbidden, suppressed, or simply forgotten. This isn’t the kind of thing you can look up without knowing exactly what you’re looking for. In the majority of cases, using this kind of magic counts as a breaking point for yourself and possibly for others depending on what it is. You can find the currently known forms in Forbidden Knowledge.