This dissertation discusses studies on the physical properties of poly(ether ether ketone) (PEEK). Several investigations involving the crystallization and melting behavior of PEEK, crystallization of PEEK on carbon fibers, and uniaxial draw of PEEK are presented. The double-melting behavior of isothermally crystallized PEEK was investigated using differential scanning calorimetry (DSC) and wide and small-angle X-ray scattering. The double-melting was found to be due to a crystal reorganization on heating. The low and high-melting endotherms are the sum of four contributions: Melting of the original crystals, their recrystallization, remelting of recrystallized crystals and melting of core crystals. Material parameters such as the thermodynamic melting point (384, 389$\sp\circ$C) and surface free energy (39 erg/cm$\sp2$) of the PEEK crystal were measured. The isothermal and non-isothermal crystallization of PEEK was found to depend on the previous thermal history. This was explained by a persistence of small residual crystalline regions up to the thermodynamic melting point, at which the infinitely large and perfect crystals melt. The crystallization of PEEK on carbon fibers was studied by DSC, electron and optical microscopy. The control, characterization, and effect of the crystalline interface between PEEK and carbon fiber were investigated. The carbon fiber surface was found to compete with nuclei in the PEEK matrix for crystallization growth. Reducing the number of nuclei in the matrix by long preheating favored PEEK crystallization on the carbon fiber, resulting in about 2 times stronger interfacial bond as indicated by transverse tensile tests. PEEK films and rods were solid-state extruded at 154 and 310$\sp\circ$C. The tensile mechanical properties were improved by drawing. The modulus and strength were increased up to 6.5 GPa and 600 MPa, respectively. The structural evolution of PEEK on drawing was studied using wide-angle X-ray diffraction and birefringence. The c axis crystal orientation function (up to 0.67) and birefringence (up to 0.30) were increased with draw ratio.