Real Algebraic Geometry for Applications. Real algebraic geometry is a fundamental input for many applications of algebraic geometry. Its goals and methods are distinct from classical algebraic geometry, and it may be studied independent of other courses in algebraic geometry. I expect to cover topics such as real solutions to systems of equations, including upper and lower bounds and algorithms for real solutions. Another topic I will cover particular to real algebraic geometry is positivity and sums of squares, which is important for optimization, and I expect to also discuss real toric varieties, which underly some objects in several different application areas. This would be based on parts of my book "Real solutions to Equations from Geometry" and three relevant chapters in another book "Algebraic Geometry for Applications" that is now a completed manuscript. Both texts will be available to class participants in .pdf form. The expected background would be a graduate course in algebra.