Sheaves were introduced in 1946 by Jean Leray. Initially, sheaf theory was conceived as an instrument in homology theory and analysis. In the 50s and 60s these objects found applications in algebraic geometry (initially by Grothendieck) and various other areas of modern mathematics.
We will define a sheaf, provide several motivational examples, and also explain sheaf maps (by focusing on injectivity, surjectivity and exactness). Cech cohomology with respect to a cover will be first introduced and later the general Cech cohomology of a topological space. As time allows, we will draw relations between better known (co)homology theories and give more examples.
The talk should be accessible (elementary geometry and topology required).