The main objective of this course is to familiarize the students with the basic 3 heat transfer modes, namely conduction, convection and radiation, which are common in aerospace systems. The students are also equipped with the ability to identify the existing heat transfer mode(s) on a given problem, and then to analyze the problem by determining the involved heat transfer rates or temperature distributions. The relevant system of equations or differential equations is formed simply by the conservation of energy principle applied to a control volume of finite size or differential size. Following the introduction of Fourier's law for heat conduction, and derivation of the general heat diffusion equation in three dimensions, equations are simplified for one-dimensional problems. Applications to plane walls, with and without thermal energy generation (heat sources), extended bodies (fins), and non-uniform cross sections with quasi one-dimensional approach are made. The concept of equivalent thermal circuit and thermal resistance to conduction heat transfer is introduced. While solving one-dimensional conduction problems with convection over a surface and/or radiation, Newton's law of cooling for convection heat transfer that develops across the thermal boundary layer and/or the black body radiation formula are used for providing the necessary boundary condition at the surface. Following one-dimensional problems, an analytical solution method is taught for treating two-dimensional linear conduction problems without volumetric heat generation. Fundamental knowledge for drawing constant temperature lines (isotherms) and heat flow lines (adiabats) is also provided to appreciate heat transfer phenomena across 2-D bodies. Transient conduction is treated analytically for complex shapes using the lumped capacitance method, and for simple shapes with 1-D conduction solving the full diffusion equation. The use of the non-dimensional Biot number is explained in transient conduction problems. The convection heat transfer mode is observed extensively in aerospace applications. Regarding this heat transfer mode, the fundamental physics pertaining to it is discussed first. For this velocity and thermal boundary layer equations are derived, and then non-dimensionalized, leading to the definitions of the Reynolds number, Prandtl number. By equating the conduction heat transfer at the surface but on the fluid side to convection heat transfer definition the so-called Nusselt number is obtained and this is shown to equal nothing but the fluid's dimensionless temperature gradient at the surface. Both analytical and experimental functions are given for the Nusselt number for various flow configurations. Internal flow convection problems are also treated. Free convection is shown to exist when gravitational effects are important. Relevant dimensionless parameters are discussed and Nusselt number correlations are given for some simple configurations, such as flat plate and horizontal infinite cylinder.  Fundamental concepts of radiation heat transfer are taught.