Rational Points and Arithmetic of Fundamental Groups : Evidence for the Section Conjecture Part I Foundations of Sections 1 Continuous Non abelian H1 with Profinite Coefficients. 2 The Fundamental Groupoid 3 Basic Geometric Operations in Terms of Sections 4 The Space of Sections as a Topological Space 5 Evaluation of Units 6 Cycle Classes in Anabelian Geometry 7 Injectivity in the Section Conjecture Part II Basic Arithmetic of Sections 7 Injectivity in the Section Conjecture 8 Reduction of Sections 9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers Part III On the Passage from Local to Global 10 Local Obstructions at a p adic Place 11 Brauer Manin and Descent Obstructions 12 Fragments of Non abelian Tate Poitou Duality Part IV Analogues of the Section Conjecture 13 On the Section Conjecture for Torsors 14 Nilpotent Sections 15 Sections over Finite Fields 16 On the Section Conjecture over Local Fields 17 Fields of Cohomological Dimension 1 18 Cuspidal Sections and Birational Analogues The section conjecture in anabelian geometry announced by Grothendieck in 1983 is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012 its study has revealed interesting arithmetic for curves and opened connections for example to the question whether the Brauer Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then arithmetic assumptions on the base field are imposed and the local to global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension