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While analyzing second order thermodynamical phase transitions, Lev Landau(the famous Russian physicist) introduced a very vital concept, the concept ofan "order parameter". This not only amalgamated the previous fragmentarytheoretical understanding of phase transitions (an arsenal of mean-fieldtheories) but also it put forward the important theory of "spontaneous symmetrybreaking". Today, order parameter concept is a paradigm both in condensedmatter physics and in high energy physics, and Landau theory is a pinnacle ofall mean-field theories. Mean field theories are good qualitative descriptorsof the phase transition behavior. But all mean-field theories (includingLandau's theory) fail at the critical point (the problem of large correlationlength). The problems with large correlation length in quantum many-bodysystems are the hardest problems known in theoretical physics (both incondensed matter and in particle physics). It was Ken Wilson's physicalinsights and his powerful mathematical skills that opened a way to the solutionof such hard problems.  This manuscript is a perspective on these issues. Starting with simpleexamples of phase transitions (like ice/water; diamond/graphite etc.) weaddress the following important questions: Why does non-analyticity (sharpphase transitions) arise when thermodynamical functions (i.e., free energiesetc) are good analytic functions? How does Landau's program unify all theprevious mean-field theories? Why do all the mean-field theories fail near thecritical point? How does Wilson's program go beyond all the mean-fieldtheories? What is the origin emergence and universality?

Thermodynamical Phase transitions, the mean-field theories, and the renormalization (semi)group: A pedagogical introduction