(Topics) Fundamentals of geometry, geometric algebra, theory of circles, constructions for inscribed and circumscribed figures, theory of abstract proportions, similiar figures and proportions in geometry, fundamentals of number theory, continued proportions in number theory, number theory, classification of incommensurables, solid geometry, measurement of figures, regular solids.

(Topics) Introduction to manifolds, tangent vectors and tangent bundles, algebra of vector fields, Lie derivatives, algebraic language in geometry, differential forms on manifolds.

(Topics) Differentiable manifolds, tangent space and tangent bundles, Riemannian manifolds, the Levi-Civita connection, geodesics, the curvature tensor, curvature and local geometry.