Are there any books written using dialogues? Last year I read Questions And Answers In School Physics. The book is based on a dialogue between a student and a teacher. A lot of concepts and ideas are seamlessly driven by the dialogue. I found the presentation to be lucid and pedagogical.
I am wondering if there is books with a similar style but for mathematics.
 A: Lakatos' Proofs and Refutations is a set of dialogues about increasingly general versions of Euler's formula.  Most people read it for the philosophy, not the mathematics, but I don't see why one couldn't go the other way.
Also, there are a large number of texts that exposit via pedagogically-motivated exercises, but don't involve multiple interlocutors.  I don't know if you consider these to be "generalized dialogues," but if you do, then consider Arnol'd and Alekseev's The Abel Theorem in Problems.
A: Conics by Keith Kendig is written as a series of dialogues between three characters : Student, Teacher and Philosopher. Student with fresh curiosity, Teacher with an open mind and ability to make connections and Philosopher picking on subtle ideas - these three personalities together develop and explore the content.
There are lots of examples covered and several exercises are given at the end of each chapter.
A: The series Math Girls by Hiroshi Yuki is both amusing and instructive. We explore together with at first two later three female students some highlights in mathematics like Fermat's last theorem or Gödel's incompleteness theorems.
Currently there are four volumes in this series, the first  with this MAA review.
A: There's always Philip J. Davis and Reuben Hersh's, "The Mathematical Experience".
A: Géométrie plane by Delessert has dialogues between the author and a character named Zosime, in which Zosime challenges the author on various points.
A: The popular mathematics book Dialogues on Mathematics (original title: Dialoge über Mathematik) by Alfréd Rényi is a set of fictional dialogues about the nature of mathematics between some historical characters (Socrates and Hippocratis in the first chapter, Archimedes and Hieron in the second one, and Torricelli, Niccolini and Galileo in the last chapter).
A: The book The Square Root of 2: A Dialogue Concerning a Number and a Sequence by David Flannery is, as the title would suggest, written as a dialogue between a teacher and a student. It is quite well done in that it is easy to follow and covers a broad range of mathematical ideas.
A: The Number Devil: A Mathematical Adventure is for younger readers, ages 11–16 or so.  The main character, Robert, has a series of twelve dialogues about mathematics with the titular Number Devil.  They discuss prime numbers, infinity, the fibonacci numbers, and many other topics.
A: Game Theory and Mutual Misunderstanding: Scientific Dialogues in Five Acts by Mamoru Kaneko.

This book consists of five acts and two interludes, which are all
written as dialogues between three main characters and other
supporting characters. Each act discusses the epistemological,
institutional and methodological foundations of game theory and
economics, while using various stories and examples. A featured aspect
of those discussions is that many forms of mutual misunderstanding are
involved in social situations as well as in those fields themselves.
One Japanese traditional comic story called the Konnyaku Mondo is
representative and gives hints of how our thought is constrained by
incorrect beliefs. Each dialogue critically examines extant theories
and common misunderstanding in game theory and economics in order to
find possible future developments of those fields.

A: Michael Negnevitsky - Artificial Intelligence. A Guide to Intelligent Systems.
It is written in the form of questions and answers. In my opinion, it is one of the best books on the topic.
A: I don't think if it suits the needs, but Logicomix by Apostolos Doxiadis and Christos Papadimitriou seems to me to be a great comics book dealing about the history and some concepts of Logic.
A: Donald Knuth's Surreal Numbers: How two ex-students turned on to pure mathematics and found total happiness  is an introduction to Conway's construction of real numbers as positions in certain two-player games.  It's very readable and it's written as a series of dialogues between the titular characters.
An unpublished French translation is available online.
A: Lev Tarasov's Calculus: Basic Concepts for High School is a Soviet classic.
