This book deals with classical questions of Algebraic Number Theory concerning the interplay between units, ideal class groups, and ramification for relative extensions of number fields. It includes a large collection of fundamental classical examples, dealing in particular with relative quadratic extensions as well as relative cyclic extensions of odd prime degree. The unified approach is exclusively algebraic in nature.Contents: The Exact Hexagon — The Group R0(E/F)The Group R1(E/F)Some Facts from Class Field TheoryDetermination of R0(E/F)Determination of R1(E/F)R0(E/F), R1(E/F) for S-IntegersThe Homomorphism C(F) → C(E)Unramified Cyclic ExtensionsRamified Cyclic ExtensionsRelative Quadratic Extensions — Hilbert SymbolsThe Narrow Class GroupSigns of UnitsCM-ExtensionsThe Kernel of C(F) → C(E)Units with Almost Independent SignsParity of the Relative Class NumberExistence of Quadratic ExtensionsQuadratic Extensions of Q — Cyclic 2-Primary Subgroups of C(E)Elementary Abelian 2-Primary Subgroups of C(E)Imaginary Biquadratic Extensions of QReal Biquadratic Extensions of QExamplesNon-Abelian Biquadratic Extensions of QThe Sets A+(2) and A-(2)The 2-Primary Subgroup of K2(0)Trivial Galois Action on C(E)Readership: Mathematicians.Key Features:A novel handbook of practical points for budding scientists contemplating a career in biomedical researchProvides practical tools for scientific writing and the meaning of the scientific publication with examples and personal experiences from the author and other scientistsThe process of grant writing is expertly dissected in this book, with practical guidelines on how to write successful grant proposals