Analytic Number Theory (Iwaniec, Kowalski)

Analytic Number Theory: An Introductory Course (Bateman, Diamond)

Problems in Analytic Number Theory (Murty)

Arithmetical Functions (Chandrasekharan)

Elementary Number Theory (Burton)

Geometric and Analytic Number Theory (Schoissengeier, Taschner)

Handbook of Number Theory I (Sándor, Mitrinovic, Crstici)

Handbook of Number Theory II (Sandor, Crstici)

Introduction to Arithmetical Functions (McCarthy)

Multiplicative Number Theory (Davenport)

Multiplicative Number Theory I: Classical Theory (Montogomery, Vaughan)

Number Theory Revealed: A Masterclass (Granville)

Problems in Algebraic Number Theory (Murty, Esmonde)

Summing It Up: From One Plus One to Modern Number Theory (Ash, Gross)

The Distribution of Prime Numbers (Koukoulopoulos)

Un cours de theorie analytique des nombres (Kowalski)

Un Parcours Explicite en Théorie Multiplicative (Ramare)

Additive Theory of Prime Numbers (Hua)

A Course in Analytic Number Theory (Overholt)

250 Problems in Elementary Number Theory (Sierpinski)

A Course in Arithmetic (Serre)

Divisors (Hall, Tenenbaum)

Number theory Vol 2_Analytic and Modern Tools (Cohen)

Number Theory: An Introduction via the Density of Primes (Fine, Rosenberger)

The Great Prime Number Race (Plymen)

Complex Analysis with Applications to Number Theory (Shorey)

Number Theory and its Applications (Li, Wang, Kanemitsu)

Number Theory and its Applications II (Li, Wang, Kanemitsu)

An Open Door to Number Theory (Campbell)

Opera de Cribo (Friedlander, Iwaniec)

Sieves in Number Theory (Greaves)

Prime-Detecting Sieves (Harman)

A Higher-Dimensional Sieve Method (Diamond, Halberstam, Galway)

Sieve Methods (Halberstam, Richert)

An Introduction to Sieve Methods and their Applications (Cojocaru, Murty)

Arithmetical Aspects of the Large Sieve Inequality (Ramare)

Sieve Methods, Exponential Sums, and their Applications in Number Theory (Greaves, Harman, Huxley)

Analytic Methods for Diophantine Equations and Diophantine Inequalities (Davenport)

The Hardy-Littlewood Method (Vaughan)

Goldbach’s Problem: Selected Topics (Rassias)

The Goldbach Conjecture (Wang)

Problems in the Theory of Modular Forms (Murty)

Introduction to the Spectral Theory of Automorphic Forms (Iwaniec)

Six Short Chapters on Automorphic Forms and L-functions (Dou, Zhang)

Some Applications of Modular Forms (Sarnak)

Spectral Methods of Automorphic Forms (Iwaniec)

Spectral Theory of the Riemann Zeta-Function (Motohashi)

The 1-2-3 of Modular Forms: Lectures at a Summer School in Nordfjordeid, Norway (Bruinier, van der Geer, Harder, Zagier)

Topics in Classical Automorphic Forms (Iwaniec)

A First Course in Modular Forms (Diamond, Shurman)

Harmonic Maass Forms and Mock Modular Forms: Theory and Applications (Bringmann, Folsom, Ono, Rolen)

Modular Forms and Fermat’s Last Theorem (Cornell, Silverman, Stevens)

Modular Functions and Dirichlet Series in Number Theory (Apostol)

Area, Lattice Points, and Exponential Sums (Huxley)

Character Sums with Exponential Functions and their Applications (Konyagin, Shparlinski)

Trigonometric Sums in Number Theory and Analysis (Arkhipov, Chubarikov, Karatsuba)

Exponential Sums and their Applications (Korobov)

Van der Corput’s Method of Exponential Sums (Graham, Kolesnik)

The Theory of the Riemann zeta-Function (Titchmarsh, Heath-Brown)

Equivalents of the Riemann Hypothesis I: Arithmetic Equivalents (Broughan)

Equivalents of the Riemann Hypothesis II: Analytic Equivalents (Broughan)

Lectures on the Riemann Zeta Function (Iwaniec)

Exploring the Riemann Zeta Function (Montgomery, Nikeghbali, Rassias)

Diophantine Inequalities (Baker)

Number Theory - Diophantine Problems, Uniform Distribution and Applications (Elsholtz, Grabner)

A royal road to algebraic geometry (Holme)

Algebraic Curves and Riemann Surfaces (Miranda)

Algebraic geometry (Milne)

Algebraic geometry and arithmetic curves (Liu)

Algebraic Geometry: A Problem Solving Approach ()

Algebriac geometry (Gathmann)

Basic Algebraic Geometry 2: Schemes and Complex Manifolds (Shafarevich)

Basic Algebraic Geometry I: Varieties in projective space (Shafarevich)

Classical Algebraic Geometry: A modern view (Dolgachev)

Elementary Algebraic Geometry (Kendig)

Enumerative Geometry (Gathmann)

Introduction to Algebraic Geometry (Dolgachev)

Lectures on curves, surfaces and projective varieties: A classical view of algebraic geometry (Beltrametti, Carletti, Gallarati, Bragadin)

Plane Algebraic Curves (Fischer)

Kowalski: https://people.math.ethz.ch/~kowalski/lecture-notes.html

Hildebrand: https://faculty.math.illinois.edu/~hildebr/

Kevin Ford: https://faculty.math.illinois.edu/~ford/

Koukoulopoulos: https://dms.umontreal.ca/~koukoulo/

Salamon: https://people.math.ethz.ch/~salamon/

Shparlinski: Problems in exponential and character sums

Keith Conrad: https://kconrad.math.uconn.edu/blurbs/

Link to AMS Student Mathematical Library here

Analysis and Linear Algebra: The Singular Value Decomposition and Applications (Bisgard)

A First Course in the Calculus of Variations (Kot)

A Primer on the Calculus of Variations and Optimal Control Theory (Mesterton-Gibbons)

A User-friendly Introduction to Lebesgue Measure and Integration (Nelson)

A Veiw From the Top (Iosevich)

Asymptopia (Spencer)

Elliptic Curves, Modular Forms, and Their L-functions (Lozano-Robledo)

Galois Theory for Beginners_ A Historical Perspective (Bewersdorff)

Harmonic Analysis, From Fourier to Wavelets (Pereyra, Ward)

Heads or Tails: An Introduction to Limit Theorems in Probability (Lesigne)

Invitation to Ergodic Theory (Silva)

Lectures on Contemporary Probability (Lawler, Coyle)

Number Theory in the Spirit of Ramanujan (Berndt)

Probability Tales (Grinstead, Peterson, Snell)

Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (Kaczor, Nowak )

Problems in Mathematical Analysis II: Continuity and Differentiation (Kaczor, Nowak)

Problems in Mathematical Analysis III: Integration (Kaczor, Nowak)

Random Walk and the Heat Equation (Lawler)

The Game's Afoot! Game Theory in Myth and Paradox (Mehlmann)

The Prime Numbers and Their Distribution (Tenenbaum, France)

Duality in Analytic Number Theory (Elliott)

The Dispersion Method in Binary Additive Problems (Linnik)

The Distribution of Prime Numbers_Large Sieves and Zero-density Theorems (Huxley)

The Large Sieve and its Applications_Arithmetic Geometry, Random Walks and Discrete Groups (Kowalski)

Additive Combinatorics (Tao, Vu)

Quantitative Arithmetic of Projective Varieties (Browning)

Representations of Integers as Sums of Squares (Grosswald)

Асимптотический закон распределения простых чисел (Balazard) (A complete elementary proof of PNT)

Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Nathanson)

Analytic Number Theory: A Tribute to Gauss and Dirichlet (Duke, Tschinkel)

Combinatorial Number Theory and Additive Group Theory (Ruzsa)

Equidistribution in Number Theory, An Introduction (Granville, Rudnick)

Logical Number Theory I: An Introduction (Smorynski)

Exponential Diophantine Equations (Shorey, Tijdeman)

Linear Forms in Logarithms and Applications (Bugeaud)

Closing the Gap (Neale)

Common Sense Mathematics: Second Edition (Bolker, Mast)