We study local aspects of the Geometric Langlands Program following the book by Edward Frenkel “Langlands Correspondence for Loop Groups” (CUP, 2007). Our aim in this term is to understand the center of a certain category of modules over the central extension (of critical level) of the loop Lie algebra g((t)). This center turns out to be the algebra of functions on a space of ‘Opers’ whose structure group is the Langlands dual group to G.