This text was designed for an IBL approach to Introduction to Geometries and covers geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and...This text was designed for an IBL approach to Introduction to Geometries and covers geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry. Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite.