Course based on the following: 

 Normal varieties:

Normal varieties, Weil divisors and canonical divisors: 
http://math.mit.edu/~mckernan/Teaching/07-08/Autumn/18.735/l_2.pdf
 http://math.mit.edu/~mckernan/Teaching/10-11/Spring/18.726/l_11.pdf
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Andreatta, Marco and Tasin, Luca, Fano-mori contractions of high length on projective varieties with terminal singularities
Bull. Lond. Math. Soc. 2014

Arbarello, Bruno, Farkas, Sacca', EXPLICIT BRILL-NOETHER-PETRI GENERAL CURVES, 2016

Dolgacev, Igor, Weighted Projective Spaces: http://www.math.lsa.umich.edu/~idolga/weighted82.pdf: 1.1, 1.2.2, 1.2.2, 1.2.3, 1.2.5

Fujino, Osamu,  What is log terminal? 
Flips for 3-folds and 4-folds,  49--62, Oxford Lecture Ser. Math. Appl., 35, Oxford Univ. Press, Oxford,  2007.

Fujino, Osamu, Fundamental theorems for the log minimal model program, 201x 

Fujino, Osamu ;  Mori, Shigefumi,  A canonical bundle formula.
 J. Differential Geom.  56  (2000)

Hacon, Christopher D. ;  Kova'cs, Sa'ndor J.  Classification of higher dimensional algebraic varieties.
Oberwolfach Seminars, 41. Birkhäuser Verlag, Basel,  2010. x+208 pp. ISBN: 978-3-0346-0289-1 

Kolla'r, Ja'nos ;  Mori, Shigefumi . Birational geometry of algebraic varieties.
With the collaboration of C. H. Clemens and A. Corti.
Translated from the 1998 Japanese original.
Cambridge Tracts in Mathematics, 134. Cambridge University Press, Cambridge,  1998. viii+254 pp. ISBN: 0-521-63277-3 

Kolla'r, Ja'nos . Singularities of the minimal model program.
With a collaboration of Sa'ndor Kova'cs.
Cambridge Tracts in Mathematics, 200. Cambridge University Press, Cambridge,  2013. x+370 pp. ISBN: 978-1-107-03534-8 
		

 Kolla'r, Ja'nos . Lectures on resolution of singularities.
Annals of Mathematics Studies, 166. Princeton University Press, Princeton, NJ,  2007. vi+208 pp. ISBN: 978-0-691-12923-5; 0-691-12923-1 

Kolla'r, Ja'nos ;  Smith, Karen E. ;  Corti, Alessio . Rational and nearly rational varieties.
Cambridge Studies in Advanced Mathematics, 92. Cambridge University Press, Cambridge,  2004. vi+235 pp. ISBN: 0-521-83207-1 	

Kolla'r, Ja'nos . Singularities of pairs.
 Algebraic geometry?Santa Cruz 1995, 
 221--287, Proc. Sympos. Pure Math., 62, Part 1, Amer. Math. Soc., Providence, RI,  1997. 

Kova'cs, Sa'ndor J: Singularities of stable varieties

Kova'cs, Sa'ndor J: Young person?s guide to moduli of higher dimensional varieties

Lazarsfeld, Robert . Positivity in algebraic geometry. I, II.
Classical setting: line bundles and linear series.
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of
 Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd
 Series. A Series of Modern Surveys in Mathematics], 48. Springer-Verlag, Berlin,  2004. xviii+387 pp. ISBN: 3-540-22533-1 

Looijenga, Eduard J. N.  Isolated singular points on complete intersections.
Second edition.
Surveys of Modern Mathematics, 5. International Press, Somerville, MA; Higher Education Press,
 Beijing,  2013

McNeal, Jeffery and Musta{\c{t}}{\u{a}}, Mircea (editors) , Analytic and algebraic geometry, IAS/Park City Mathematics Series, Common problems, different methods, Lecture notes from the Graduate Summer School Program held in Park City, UT, 2008
American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2010

Morriosn, David; Taylor, Washington, Sections, multisections, and U(1) fields in F-theory, 2014

Reid, Miles, Canonical 3-folds, Journ\'ees de G\'eometrie Alg\'ebrique d'Angers, Juillet
      1979/Algebraic Geometry, Angers, 1979.

Reid, Miles, Young Person Guide to Canonical Singularities.

Reid, Miles, Chapters on surfaces