The present book is the English translation of Louis Hjelmslev’s lectures on glossematics, the theory of language developed in the forties by him and Hans Jørgen Uldall, and taught at the University of Copenhagen in 1942-43, thoroughly taken down in shorthand by his student Harry Wett Frederiksen. The document, unpublished so far, is one-of-a-kind in its pedagogical dimension, as it aims to introduce students, and now readers, to the glossematician’s workshop, informally discussing its theoretical framework, the operations employed in description and the reasons why such operations were devised via a concrete analysis of Hans Christian Andersen’s fairy-tale "The Sweethearts". Overall, the document offers a unique glimpse into the machinery of one of the most epistemologically aware and rigorous theories of language developed in the 20th century.