The concept of repression
Nietzsche's overarching idea highlights how modernity is linked with repression of our "inner-life" (consciousness). Nietzsche is crucial for paving the way for other thinkers such as Sigmund Freud and Max Weber.
Critical theory
Both Nietzsche and Freud are known as "critical" theorists because their mission was to scrutinize the human consciousness.
Other 20th century thinkers such as Hegel and Marx have a clear idea of a "good society" from which they criticize the shortcomings of our actual society.
The goal of the Genealogy of Morality
The book's primary goal is to offer critical scrutiny of the human mind being explicit about not taking any side in the debate. The critical scrutiny of the human mind extends into society to the point where Nietzsche is interested in understanding our definition of good and how that shaped society.
The genealogy method is one where without taking either side of the good/bad debate, you look back at history and see how we defined good and bad in various scenarios (and how that changed over time). For example, looking back to antiquity, you quickly see examples such as slavery, which was seen as "good" in stark contrast with today's age.
Revolt against religious upbringing
To understand Nietzsche, we have to look at his very religious upbringing and how most of his intellectual development can be seen as a rebellion against that early part of life.
The Birth of the Tragedy
Nietzsche was heavily inspired by Greek culture, which he appreciated due to the culture's emphasis on heroic acts. In The Birth of the Tragedy, Nietzsche sees human history as driven by the struggle between the Dionysian (instinct/emotion) and Apollonian (reason) principle. Using this framework, we can understand the project of Enlightenment as a triumph of the Apollonian principle over the Dionysian principle. Nietzsche rejects the excessive rationalism of the Enlightenment and is leaning towards of synthesis of emotion and reason (than either one in particular).
Thus Spoke Zarathustra
In the book, Nietzsche attempts to find a path forward that does not fall into the pitfalls of Judeo-Christian morality but does not reject everything by turning to nihilism. Here, he develops the idea of the Ubermensch, who can rise above his circumstances and take matters and control into his own hands.
Slave morality
Morality in antiquity indicated that the people in power were "good" while those under subjugation were "bad." The slave morality ushered in by the Jewish revolt radically altered those values. The Judeo-Christian tradition stipulates that the only "good" people in a society are powerless and those who suffer.
Modernity's defining feature
Looking at the depictions of the Greek heroes, Nietzsche could not help but wonder whether modernity has ushered in mediocrity with its docile doctrine.