Stirner is rather accessible so long as you remain cognizant of his irony and sarcasm throughout and remember to perhaps not take him literally at times even when you ought to take him seriously. While there is context that can enrich your understanding of Stirner and the milieu he was situated in, it is ultimately not necessary to understand the philosophy
of his works. If anything, it is easier to understand him now than back then because Stirner has come to be known as a forerunner for much of the philosophy that developed in the 20th century and has transformed culture into the one you now live in, especially in the latter half and in postmodern philosophy, such as structuralism and post-structuralism and some of the radical nominalist / constructivist ideas which became in vogue. Basically, if you know who Jesus is, you have some vague familiarity with the fact that Stirner was a 19th-century writer who had some association with Hegelian thought, you're more than set. And even those are optional!
If you want some context for him, though, Hegel and the Young Hegelians in particular, along with German idealism and the Enlightenment-era thinking more generally, is where to go. Given that these are some of the big thinkers of history and Hegel is basically one of the absolutely most difficult philosophers to read and understand in history (even though Hegel's writing style is surprisingly accessible), it is quite fortunate that understanding Stirner does not require this yet is enriched by it.
I will note, however, that while Stirner is accessible in terms of reading and understanding his words without being burdened endless jargon and insular academic philosophical debates (he really cuts through all that), Stirner can be extremely difficult to really get by someone who is unwilling or unable to have some of their most sacred cows and ideological idols reduced to mere hallucinations of the mind. Stirner is also hard to understand if you naïvely take him at face value and lack the ability to read the smirk in his words (Just look at that smirk! He's having the time of his life!). Unlike many philosophers, or at least unlike the public perception of philosophers, Stirner is much more flippant and satirical in his language, to the point of stunning hyperbole. This is why I recommend what I did in my first sentence: if you don't, you can easily come away from a book like The Unique and its Property
thinking that this man is an egotistic lunatic who literally considers you his property, believed everyone around him to be possessed by ghosts, views himself as the creator of all existence, and bases all his outrageously bold claims on absolutely nothing at all. The fact that the older English translations (not the Wolfi one I linked below) are not very good only exacerbates this.
These peculiarities are principally because of Stirner's milieu, but also because his The Unique and Its Property
is meant to be both a polemic against many of his contemporaries and the prevailing new philosophical movement of his time (Hegelianism) as well as a parody of Hegelian thought (despite having an implicit anti-/Hegelian character). While polemic is common in philosophy, especially philosophy from and after the Enlightenment; and even parody and satire are not uncommon, albeit less common, with Voltaire being a major Enlightenment thinker who used it; they tend to contrast with what one might expect from philosophical treatises, especially if you're new to philosophical literature, and they tend to be nowhere near as outrageous as Stirner takes it. The closest parallel I can draw here in philosophy would probably be over 2,000 years earlier, in ancient Greece, with the Sophist Gorgias of Leontini's lost work On Nothing
as a satirical critique and response to Parmenides' On Nature
, arguing that not only does nothing exist, but even if
anything does, it is unknowable to us, and even if
it is knowable to us it is incomprehensible to us, and even if
it is comprehensible it is unable to be communicated, and even if
it is communicable it is unable to be understood. In a sense, Stirner takes after that
critical undercurrent in philosophy and so considering him in that context may avoid some of the more common pitfalls with reading his works.
All this makes Stirner the more livelier a writer to read, though, which can make his work engaging even if difficult, even for the lay reader. So give it a shot, it's free to read on The Anarchist Library:
The Unique and Its Property
by Max Stirner (1845), trans. Wolfi Landstreicher (2017): https://theanarchistlibrary.org/library/max-stirner-the-unique-and-its-property
by Max Stirner (1845), trans Wolfi Landstreicher (2011?): https://theanarchistlibrary.org/library/max-stirner-stirner-s-critics
Stirner wrote other works, including on education (he was a teacher at a girl's gymnasium before resigning in anticipation of the controversy of his publications) and "philosophical reactionaries" among others. The two most relevant to post-left theory and philosophy (and radical nihilist philosophy generally), as well as the lasting philosophical legacy of Stirner, are the two linked above.