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It is said that the current global population could be included as living at present with an "international average economic level", when the prevailing interest and performance is to satisfy the spiritual, cultural needs; towards scientific, artistic and ethical creation. Only then, we will create the possibility of enjoying a more human world, where the transmission, the appropriation of knowledge and its application will be the "advanced education" in its highest expression. In Latin American and the Caribbean, higher education grew sixty times in the last six decades, a trend that will continue the enhancement of the multiplication and diversification of its organizations, by increasing offers; modifying the student composition and those of the new academic environments. In our region, it goes from the most legitimate government universalization of higher education to the multiple variants of the hybrid assembly determined by privatization, by the marketing costs. In an equivalent time, by walking through the ways of equity, the Cuban higher education shows at present significant achievements, both in consolidating its links and commitments with it social, political and economic life, as being oriented to excellence, of its process and results. According to the formerly stated, now this paper orders its contents through the following groups: 01- Universalization of the university: equity-quality in higher education. 02- Elite Model , Mass Model, Universal Model.03- Tertiary Coverage Rates in the Current World: Statistical Reliability and Calculus Difficulties. 04- Cuba in figures. [ABSTRACT FROM AUTHOR]