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The aim of this paper is to discuss some basic notions regarding genericglass forming systems composed of particles interacting via soft potentials.Excluding explicitly hard-core interaction we discuss the so called `glasstransition' in which super-cooled amorphous state is formed, accompanied with aspectacular slowing down of relaxation to equilibrium, when the temperature ischanged over a relatively small interval. Using the classical example of a50-50 binary liquid of N particles with different interaction length-scales weshow that (i) the system remains ergodic at all temperatures. (ii) the numberof topologically distinct configurations can be computed, is temperatureindependent, and is exponential in N. (iii) Any two configurations in phasespace can be connected using elementary moves whose number is polynomiallybounded in N, showing that the graph of configurations has the `small world'property. (iv) The entropy of the system can be estimated at any temperature(or energy), and there is no Kauzmann crisis at any positive temperature. (v)The mechanism for the super-Arrhenius temperature dependence of the relaxationtime is explained, connecting it to an entropic squeeze at the glasstransition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities