This module investigates one of humanity’s strangest, most intractable concepts: the concept of infinity. It hurts the mind to think of anything limitless. It creates all sort of troublesome paradoxes. Yet logic seems to compel us to contemplate the possibility of infinite space, and also infinitesimal space – the infinitely small – and also limitless time: eternity. The imagination is excited by these things as much as the intellect is pained. Infinity is an important theme in human art, philosophy and theology. Students on this course will develop their dialectic skills, their appreciation of literature, their philosophical subtlety, and their writing skills. They will end by being able to express sophisticated views about the issue of infinity, from many angles and in different modes. This lecture gives a complex overview of the mysterious concept of infinity. The start of the syllabus investigates whether infinity exists at all in our physical world. Even though we give a positive answer to the aforementioned question, actual infinity is not ubiquitous in our life. In science, it is more common that we artificially create infinities to use it as a tool to tackle problems. The second part of syllabus walks on this direction, taking a detour into sequences and analysis. Finally, the plausibly most interesting and useful part of the module contains plenty of paradoxes helping the students to get their own understanding of the real meaning of infinity.