From the reviews: "The present monograph is Part 1 of a book intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. ... This monograph written by well-known experts is an excellent presentation of Jorgensen's theory with many informative illustrations. It will be very useful for researchers working on modern problems in quasifuchsian group theory, hyperbolic and geometry and hyperbolic knot theory." (Andrei Vesnin, Zentralblatt MATH, Vol. 1132 (10), 2008)

• Jorgensen's picture of quasifuchsian punctured torus groups.- Fricke surfaces and PSL(2, ?)-representations.- Labeled representations and associated complexes.- Chain rule and side parameter.- Special examples.- Reformulation of Main Theorem 1.3.5 and outline of the proof.- Openness.- Closedness.- Algebraic roots and geometric roots.

From the reviews: "The present monograph is Part 1 of a book intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. ... This monograph written by well-known experts is an excellent presentation of Jorgensen's theory with many informative illustrations. It will be very useful for researchers working on modern problems in quasifuchsian group theory, hyperbolic and geometry and hyperbolic knot theory." (Andrei Vesnin, Zentralblatt MATH, Vol. 1132 (10), 2008)

• Jorgensen's picture of quasifuchsian punctured torus groups.- Fricke surfaces and PSL(2, ?)-representations.- Labeled representations and associated complexes.- Chain rule and side parameter.- Special examples.- Reformulation of Main Theorem 1.3.5 and outline of the proof.- Openness.- Closedness.- Algebraic roots and geometric roots.

From the reviews: "The present monograph is Part 1 of a book intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. ... This monograph written by well-known experts is an excellent presentation of Jorgensen's theory with many informative illustrations. It will be very useful for researchers working on modern problems in quasifuchsian group theory, hyperbolic and geometry and hyperbolic knot theory." (Andrei Vesnin, Zentralblatt MATH, Vol. 1132 (10), 2008)

• Jorgensen's picture of quasifuchsian punctured torus groups.- Fricke surfaces and PSL(2, ?)-representations.- Labeled representations and associated complexes.- Chain rule and side parameter.- Special examples.- Reformulation of Main Theorem 1.3.5 and outline of the proof.- Openness.- Closedness.- Algebraic roots and geometric roots.