1. Basic Principles -- 1.1. Introduction -- 1.2. The principle of virtual displacements -- 1.3. The unit force theorem -- 1.4. The unit displacement theorem -- 1.5. Energy variational principles -- 2. Fundamentals of the Finite Element Method -- 2.1. Historical development of the method -- 2.2. The concept of analysis by the finite element method -- 2.3. Energetic approaches of development of finite elements -- 2.4. Application of the unit displacement and unit force theorems -- 2.5. Energetic approach by boundary integration -- 2.6. The essence of the method -- 2.7. Isoparametric formulation -- 2.8. The direct method of development of finite elements -- 2.9. The progress of the mixed method -- 3. The Mixed Method in Analysis of Beam Systems -- 3.1. Introduction -- 3.2. Mixed beam element -- 3.3. Analysis of beam systems -- 3.4. Beam on elastic supports -- 3.5. Dynamics of beams -- 3.6. Stability of the beam systems -- 3.7. Coupled action of axial and transverse forces -- 4. Plate Bending Analysis -- 4.1. Rectangular element with independently assumed displacements and moments -- 4.2. Compatible element derived by boundary integration -- 4.3. Rectangular element derived by the direct method -- 4.4. Accuracy of the rectangular elements -- 4.5. Element for analysis of moderately thick plates -- 4.6. Isoparametric formulation -- 4.7. Quadrilateral element -- 4.8. Quadratic isoparametric element -- 4.9. Curved boundary element of complex displacement function -- 4.10. Accuracy of isoparametric elements -- 4.11. Practical application -- 4.12. Dynamics of plates -- 4.13. Stability of plates -- 5. Two-Dimensional Problems -- 5.1. Differential equations of the problems -- 5.2. Shortcomings of the previously developed elements -- 5.3. Rectangular mixed plane stress element -- 5.4. Quadrilateral element -- 5.5. Element of curved contours -- 5.6. Convergency and accuracy of the presented elements -- 6. Shells -- 6.1. Differential equations of shells -- 6.2. Mixed rectangular element -- 6.3. Analysis of dome shell -- 6.4. Analysis of cylindrical roof shell -- 6.5. Analysis of cylindrical pipe -- 6.6. Analysis of hyperbolic paraboloid shell -- 6.7. Comments and tasks for further research -- 7. Three-Dimensional Elements -- 7.1. Introduction -- 7.2. Three-dimensional elements -- 7.3. Mixed element of 36 d.o.f. -- 7.4. Prismatic element of 36 d.o.f. -- 7.5. Reduced three-dimensional element for plate bending analysis -- 7.6. Analysis of thick plates -- 7.7. Further development of three-dimensional elements -- 8. Further Development of the Finite Element Method -- 8.1. From one-dimensional to two-dimensional elements; accuracy -- 8.2. Displacement interpolation function -- 8.3. On the degrees of freedom -- 8.4. Some remarks on the application of the energy variational principles -- 8.5. The mathematical (direct) approach of development of finite elements -- 8.6. Application of the FEM for solution of different problems -- 8.7. Further development of the mixed method -- References.