Lecture 6 - Understanding the Zariski Topology on the Affine Line; The Noetherian property in Topology and in Algebra

Lecture 7 - Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity

Lecture 12 - Capturing an Affine Variety Topologically From the Maximal Spectrum of its Ring of Functions

Lecture 15 - Quasi-Compactness in the Zariski Topology; Regularity of a Function at a point of an Affine Variety

Lecture 17 - Characterizing Affine Varieties; Defining Morphisms between Affine or Quasi-Affine Varieties

Lecture 18 - Translating Morphisms into Affines as k-Algebra maps and the Grand Hilbert Nullstellensatz

Lecture 19 - Morphisms into an Affine Correspond to k-Algebra Homomorphisms from its Coordinate Ring of Functions

Lecture 20 - The Coordinate Ring of an Affine Variety Determines the Affine Variety and is Intrinsic to it

Lecture 21 - Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture; The Punctured Plane is Not Affine

Lecture 23 - Gluing (n+1) copies of Affine n-Space to Produce Projective n-space in Topology, Manifold Theory and Algebraic Geometry; The Key to the Definition of a Homogeneous Ideal

Lecture 25 - Expanding the Category of Varieties to Include Projective and Quasi-Projective Varieties

Lecture 27 - Adding a Variable is Undone by Homogenous Localization - What is the Geometric Significance of this Algebraic Fact ?

Lecture 30 - The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation !

Lecture 31 - The Field of Rational Functions or Function Field of a Variety - The Local Ring at the Generic Point

Lecture 32 - Fields of Rational Functions or Function Fields of Affine and Projective Varieties and their Relationships with Dimensions

Lecture 34 - The d-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring of a Projective Variety

Lecture 35 - The Importance of Local Rings - A Morphism is an Isomorphism if it is a Homeomorphism and Induces Isomorphisms at the Level of Local Rings