We propose TrueType Transformer (T3), which can perform character and font style recognition in an outline format. The outline format, such as TrueType, represents each character as a sequence of control points of stroke contours and is frequently used in born-digital documents. T3 is organized by a deep neural network, so-called Transformer. Transformer is originally proposed for sequential data, such as text, and therefore appropriate for handling the outline data. In other words, T3 directly accepts the outline data without converting it into a bitmap image. Consequently, T3 realizes a resolution-independent classification. Moreover, since the locations of the control points represent the fine and local structures of the font style, T3 is suitable for font style classification, where such structures are very important. In this paper, we experimentally show the applicability of T3 in character and font style recognition tasks, while observing how the individual control points contribute to classification results.