Contents 1. Introduction to the present situation in cosmology . 2. Observational data in cosmology . 2.1. The cosmic distribution of luminous matter . 2.2. T h e red shift . 2.3. Extragalactic radio sources . 2.4. Quasi-stellar sources (quasars) and quasi-stellar galaxies . 2.5. The background radiation in the Universe at radio and optical 2.6. The x-ray and y-ra; background and'cosmic rays : 3. Introductory theoretical background . 3.1, Cosmological space-time . 3.2. Red shift of spectral

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... s . 3.3. Luminosity and flux density of radiating objects , 3.4. Number counts and angular diameters 3.5. Mach's principle . 4. Evolutionary or relativistic cosmology 4.1. Exploding-type universes of Robertson-\Valker metric. . 4.2. The behaviour of exploding models at large t 4.3. Behaviour of exploding models at small t , assuming p --f +p 4.4. The background radiation in isotropic world models 4.5. Newtonian cosmology . 5. Steady-state theory , 5.1. Introduction . 5.2. The perfect cosmological principle 5.3. The C field . 5.4. hlach's principle and the creation of matter 5.5. The nature of creation , 6. Observational tests of cosmological theories 6.1. The (m, z ) relation . 6.2. The counts of radio sources . 6.3. The radiation background at radio and optical frequencies 6.4. T h e x-ray and y-ray background 6.5. Extragalactic cosmic rays and intergalactic matter 6.6. Remarks on observational tests of steady-state cosmology 7. Local effects of cosmological significance 1.4 x 106 erg cm-2 sec-l. Apparent magnitudes may be bolometric (mbol) corresponding to total apparent luminosity, visual (m.,) corresponding to apparent luminosity in the visual part of the spectrum, or photographic (wipg) correspondmg to that part of the spectrum registered on a photographic plate, They may also be measured for selected colours; for example, U denotes the apparent magnitude in the ultra-violet, B in the blue and V in the visual or yellou. t 1 parsec = 3.26 light years. 4 Absolute magnitude, denoted by M , measures intrinsic luminosity and is defined as the apparent magnitude at a distance of 10 parsec from the object. A zero absolute magnitude corresponds to an intrinsic luminosity L equal to 3 x erg sec-l. This may be compared with the Sun's total emission La = 3.9 x erg sec-'. As for apparent magnitude the absolute magnitude may be bolometric, photographic or visual, etc.