Oh dear, okay, lets see, to be very brief on the subject, from the moment the PRI "reformed" out of the PRM it wielded considerable political power being the "successors" of the mexican revolution and of policies like the Maximato, the reality of the matter is that up until the formation of the "Frente Amplio Progresista" in 1989, which was started by PRI dissidents in the first place and gathered a veritable cacophony of opposition parties into a single unified front, the PRD, there wasnt any real political opposition to the PRI party up until the 70's with Echeverria and the massacre of Tlatelolco.

The details of which are gruesome and something I personally prefer not to talk too much about, if you want an indept view of the event Elena Poniatowska's "La noche de Tlatelolco" is the seminal work on the subject.

This was followed by another massacre called "el Halconazo" in 1971, needless to say Echeverria was and is one of the most criticized and hated politicians in the history of Mexico.

This was followed by "the dog" Portillo who promised to defend the mexican peso "like a dog" in the face of an economic crisis.

Then came de la Madrid who began the practice of selling off state-owned enterprises and applying neo-liberal economic reforms, which didnt exactly pan out as expected, but more importantly, his administration completely failed to respond in any degree to the disaster that was the earthquake of 85, this earned few friends unsurprisingly.

Throughout this time the PRI applied a policy of patronage with the different state syndicates in the country, so for example Carlos Romero Deschamps from PEMEX and Carlos Jonguitud Barrios from the SNTE became incredibly rich during these periods and became deeply tied to the PRI political structure, at the same time the neo-liberal politics of de la Madrid and latter Salinas de Gortari benefited groups of bussinesmen, for example by Salina's term TELMEX a then state-owned company was sold to current richest in the planet Carlos Slim for a fraction of its value, and public funds like FOBAPROA effectively ensured banks in Mexico were unable to go bankrupt through the use of public funds.

Of course its not like all of this went smoothly, the "Frente Amplio Progresista", later the PRD launched Cuahtemoc Cardenas, son of celebrated ex-president Lazaro Cardenas as presidential candidate, which for the first time in almost a century presented a believable opposition to the PRI, unfortunately the elections were lost and the PRI won, in elections many (me included) have since decried as fraud, when the IFE's (the mexican electoral system) electronic systems went down for a moment and when they came back the PRI candidate Salinas de Gortari was suddenly ahead by several points from his opposition.

All of that follows is more contemporary and its something I really am unable to be unbiased from this point on, as this is around the time I was born and everyhting from this point on would be inevitably tainted by my experiences.

If you want further reading beyond the aforementioned La Noche de Tlatelolco I highly recommend Vargas Llosa's "The perfect dictatorship", anything by Eduardo del Rio "Rius" like "Santo PRI Libranos del PAN!" or "Ni Independencia, ni Revolución" would also do.

But honeslty?, I kind of think you'd get more information on this by asking in /r/askLatinAmerica or /r/Mexico.