1 Introduction. - 1. 1 Background of Shape Theory. - 1. 2 Principles of Allometry. - 1. 3 Defining and Comparing Shapes. - 1. 4 A Few More Examples. - 1. 5 The Problem of Homology. - 1. 6 Notes. - 1. 7 Problems. - 2 Background Concepts and Definitions. - 2. 1 Transformations on Euclidean Space. - 2. 2 Differential Geometry. - 2. 3 Notes. - 2. 4 Problems. - 3 Shape Spaces. - 3. 1 The Sphere of Triangle Shapes. - 3. 2 Complex Projective Spaces of Shapes. - 3. 3 Landmarks in Three and Higher Dimensions. - 3. 4 Principal Coordinate Analysis. - 3. 5 An Application of Principal Coordinate Analysis. - 3. 6 Hyperbolic Geometries for Shapes. - 3. 7 Local Analysis of Shape Variation. - 3. 8 Notes. - 3. 9 Problems. - 4 Some Stochastic Geometry. - 4. 1 Probability Theory on Manifolds. - 4. 2 The Geometric Measure. - 4. 3 Transformations of Statistics. - 4. 4 Invariance and Isometries. - 4. 5 Normal Statistics on Manifolds. - 4. 6 Binomial and Poisson Processes. - 4. 7 Poisson Processes in Euclidean Spaces. - 4. 8 Notes. - 4. 9 Problems. - 5 Distributions of Random Shapes. - 5. 1 Landmarks from the Spherical Normal: IID Case. - 5. 2 Shape Densities under Affine Transformations. - 5. 3 Tools for the Ley Hunter. - 5. 4 Independent Uniformly Distributed Landmarks. - 5. 5 Landmarks from the Spherical Normal: Non-IID Case. - 5. 6 The Poisson-Delaunay Shape Distribution. - 5. 7 Notes. - 5. 8 Problems. - 6 Some Examples of Shape Analysis. - 6. 1 Introduction. - 6. 2 Mt. Tom Dinosaur Trackways. - 6. 3 Shape Analysis of Post Mold Data. - 6. 4 Case Studies: Aldermaston Wharf and South Lodge Camp. - 6. 5 Automated Homology. - 6. 6 Notes. Language: English