Laflamme, ClaudeWoodrow, RobertChan, Brian2016-08-172016-08-1720162016http://hdl.handle.net/11023/3187This thesis investigates which lattices are countable sublattices of free lattices. This is equivalent to determining which lattices are sublattices of the free lattice on three generators. Our investigation is based on the following open problem (see \cite{FL}, 1995): ``Which lattices (and in particular which countable lattices) are sublattices of a free lattice?'' We describe how stronger variants of the semidistributive laws have contributed to our current understanding of sublattices of free lattices. In particular, we see how the strongest results known only apply to certain classes of countables lattices. Afterwards, we propose a strategy for analyzing the following class of countable lattices: finite width sublattices, L, of free lattices, where L is in a semidistributive variety.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Education--MathematicsFree Latticesmaster thesis10.11575/PRISM/24830