What are Descartes' three waves of doubt and his response to it?

Descartes went through three increasingly strong arguments in an attempt to bring doubt to every single thing that he knew. The first is the argument from illusion, in which he suggests that his senses may deceive him as to what he experiences (Draw diagram as a memory aid). In his next argument he strengthens this by questioning whether everything he knows and has experienced was really just a dream (another diagram). Finally, responding to the solution that God would not deceive, he argues that God may not exist, and instead an evil demon may have been deceiving him at every turn. (third diagram to represent this). Descartes solution to this issue is expressed through the phrase: cogito ergo sum - I think therefore I am. The meaning behind this is that, according to Descartes' reasoning, the evil demon can never convince him that he does not think. If he is thinks he doesn't think, he must be thinking, and so it is impossible for him not to be a thinking thing. From there he makes the simple leap that if he thinks, he must exist as a thinking thing. Whether this is a sound jump in logic is a question which explores the topic in greater depth, for exam questions which require debate and evaluation as opposed to just explaining a theory.