Theoretical astrophysicists have been developing radiative transfer theory for a long time. However, they have been primarily concerned with stellar atmospheres, within which the scattering of light is isotropic. In the atmospheres of the planets, light scattering by an elemen­tary volume is anisotropic. This fact severely complicates the theory. Nevertheless, in recent years the theory of radiative transfer for anisotropic scattering has made considerable pro­ gress and has been increasingly used in the study of planetary atmospheres. The present monograph has been written for the purpose of summarizing the results of work in this area.The monograph is concerned mainly with the theory of radiative transfer for anisotropic scattering. The first eight chapters deal with the general problem of multiple scattering of light in an atmosphere consisting of plane-parallel layers illuminated by parallel radiation.In the following two chapters, the theory is applied to the determination of the physical characteristics of planetary atmospheres. The last chapter discusses the theory of radiative transfer in spherical atmospheres, which is necessary for the interpretation of observations made from spacecraft.The emphasis in the monograph on the theory rather than its application is easily under­ stood; the theory is designed not only for the interpretation of existing observational data, but also for that to be gathered in the future. One must also bear in mind that the theory of radiative transfer is utilized in related sciences, such as meteorology and oceanology, and also in certain branches of physics and chemistry.Chapter 1 Basic Equations 11.1 The scattering of light by an elementary volume 11.2 The equation of radiative transfer 51.3 The Basic Problem 81.4 Integral equations for the Source Function 121.5 The diffuse radiation field 151.6 The case of pure scattering 191.7 Methods for solving the problem 21Chapter 2 Semi-infinite Atmospheres 242.1 The Radiation field in Deep Layers (Relative intensity of radiation) 242.2 Diffuse reflection of light 292.3 Diffuse transmission of light 352.4 The Radiation field in Deep Layers (Absolute Intensity) 412.5 The Atmospheric albedo for small true absorption 432.6 The Other Quantities in the case of small true absorption 46Chapter 3 Atmospheres of Finite Optical Thickness 523.1 Diffuse reflection and transmission of light 52 3.2 Dependence of the reflections and transmission coefficients on optical thickness 573.3 Atmospheres of large optical thickness 603.4 Asymptotic formulas for auxiliary functions 653.5 Inhomogeneous atmospheres 66Chapter 4 Atmospheres overlying a reflecting surface 744.1 Basic equations 744.2 The case of isotropic reflection 784.3 The albedo of the Atmosphere and Illumination of the surface 804.4 The spherical albedo of the planet 834.5 Specular reflection of light 86Chapter 5 General Theory 895.1 Transformation of the basic integral equation 895.2 The Auxiliary equation 935.3 The function H^{n}(𝜂) 945.4 The fundamental function 𝛷^{m}(𝜏) 995.5 Particular cases 102Chapter 6 General Theory (continued) 1076.1 Expression of the source function in terms of auxiliary functions 1076.2 The fundamental function 𝛷^{m}(𝜏, 𝜏_{0}) 1096.3 1126.4 Particular cases 1156.5 Equations containing derivatives with respect to 𝜏_{0} 1196.6 Atmospheres of large optical thickness 121Chapter 7 Linear Integral equations for the reflection and transmission coefficients 1267.1 Semi-infinite atmospheres 1267.2 The radiation intensity averages over azimuth 1317.3 Expressions in terms of the functions H^{n}(𝜂) 1337.4 The case of three-term phase function 1367.5 Numerical results 1407.6 Atmospheres of finite optical thickness 1437.7 Expressions in terms of the functions X^{m}(𝜂) and Y^{m}(𝜂) 1477.8 The case of a two-term phase function 149Chapter 8 Approximate Formulas 1538.1 The use of integral relations 1538.2 Some inequalities 1568.3 Similarity relations 1588.4 Directional averaging of the radiation intensity 1618.5 The case of pure scattering 1648.6 The Effect of the Reflection of Light by a Surface 1678.7 The radiation field for Highly anisotropic scattering 169Chapter 9 The radiation emerging from a planet 1749.1 The distribution of brightness across a planetary disc 1759.2 Dependance of planetary brightness on phase angle 1779.3 Planetary spectra for different points on the disc 1809.4 Planetary spectra for different phase angles 1859.5 polarization of light from a planet 189Chapter 10 Optical Properties of Planetary atmospheres 19510.1 Interpretation of the photometric observations of Venus 19510.2 Interpretation of polarimetric observations of Venus 19810.3 The Atmosphere of the Earth 20210.4 The Atmosphere of Mars 20510.5 The Atmospheres of Giant Planets 207Addendum 210Chapter 11 Spherical Atmospheres 21211.1 The Integral equation for the source function in the case of isotropic scattering 21211.2 The basic equations of anisotropic scattering 21811.3 Solution of the equation in particular case 22111.4 The case of an absorption coefficient exponentially decreasing with altitude 22411.5 Spacecraft observations of planets 231Concluding remarks 235Appendix 239Author Index 250Subject Index 253