From the reviews: "A transseries can be described ... as a formal object constructed from the real numbers and an infinitely large variable x using infinite summation, exponentiation, and logarithm. ... The author intends the book for non-specialists, including graduate students, and to that end has made the volume self-contained and included exercises. The book is intended for mathematicians working in analysis, model theory, or computer algebra. Algebraists should also find interest in the algebraic properties of the field of transseries." (Andy R. Magid, Zentralblatt MATH, Vol. 1128 (6), 2008)

• Orderings.- Grid-based series.- The Newton polygon method.- Transseries.- Operations on transseries.- Grid-based operators.- Linear differential equations.- Algebraic differential equations.- The intermediate value theorem.

From the reviews: "A transseries can be described ... as a formal object constructed from the real numbers and an infinitely large variable x using infinite summation, exponentiation, and logarithm. ... The author intends the book for non-specialists, including graduate students, and to that end has made the volume self-contained and included exercises. The book is intended for mathematicians working in analysis, model theory, or computer algebra. Algebraists should also find interest in the algebraic properties of the field of transseries." (Andy R. Magid, Zentralblatt MATH, Vol. 1128 (6), 2008)

• Orderings.- Grid-based series.- The Newton polygon method.- Transseries.- Operations on transseries.- Grid-based operators.- Linear differential equations.- Algebraic differential equations.- The intermediate value theorem.