Explore the fascinating world of oriented circles and their connection to relativistic geometry in this advanced mathematics lecture. Delve into topics such as homothetic centers, Monge's theorem, and the problem of Apollonius. Learn how to apply linear algebraic concepts to circle geometry and discover the geometrical interpretation of Einstein's Special Relativity. Examine the relationship between signed circles and relativistic quadrance, including the locus of circles tangent to two given ones. Investigate spheres in relativistic space and their representation in circle geometry. Gain insights into a new theorem describing the geometrical meaning of relativistic quadrance between signed circles. This comprehensive lecture covers complex material, so take your time to absorb the wealth of information presented.