Pāḷi is the 'language' the early discourses and analyses of Buddhism are recorded into. The Theravada tradition used oral transmission for centuries, but we nowadays have proofs (from archeological scrolls) that such a transmission was a lot more reliable than one would naïvely expect: we have been able to show that only a few syllables might get wronged over almost two millenia!
In a recent book, Buddhism and Pali, Prof. Gombrich (the? leading authority on Pāḷi) argued that Pāḷi might well in fact be the language the Buddha spoke, rather than an artificial language created solely for the purpose of storing knowledge.
One of the key arguments —in my view— are the weird features of the language, which makes the voluntary construction of an artificial language unlikely, in particular in the cultural context of Sanskrit, as Sanskrit has precise and rigid rules.
• If a well-established language was sought for storage, Sanskrit would simply have been chosen; language doesn't have truth-value in Buddhism, and translations were always allowed, hence Sanskrit would have been so convenient it would have won the day;
• If a competitor language had been willed into existence, to distinguish Buddhism from Brahminism, it would have… competed: it would have a precise structure, clear rules, unambiguous constructs! Pāḷi is anything but!
The irregularities, in fact, are so 'bad' that there's a strong case to suggest that it's a mix of local dialects, rather than a 'rational' construct. Pāḷi is based on Kosalī, extended by local dialects (in particular Māgadhi). There are many ways to say the same thing, sometimes many declensions for the same word (in the very same number, gender, case): the 'ablative' singular of dhamma might thus be dhammā, dhammasmā or dhammamhā while the 'locative' singular might be dhamme, dhammasmiṃ, or dhammamhi ! The 'optative' of a verb might also display similarly wide variants: first person singular might thus be bhave, bhaveyyaṃ or bhaveyyāmi.
Regardless of whether it's the language the Buddha actually spoke (and therefore the recorded speeches might be his actual speeches) or not, the earliest extent texts we have are in Pāḷi… so the most dedicated Buddhists might want to learn that language… to free themselves from the biases of translators: any translation into one's modern language might then be 'checked' whenever it seems weird, and still-untranslated commentaries might be consulted, etc. But that's when trouble begins!
Up until recently, a new course in reading Pali was probably the best textbook available, notably used by bhikkhu Bodhi for his courses available online.
There's no doubt this is a very decent book, with well chosen examples and exercises directly taken from the Theravada canon… which allows to enter directly into the texts that motivate in the first place anyone to learn Pali!
But a recent book is proving even better, in my view: reading Buddhist Pali Texts, from the Buddha Dharma center in Hongkong.
First, the 'rules' of the language are given very clearly: I'm not sure if it's better than the previous book mentioned, but it isn't worse either. For example, the declension 'tables' might be worse (less systematic), but what the declensions are used for is much better.
Second, and most importantly, vocabulary is introduced gradually, through the examples, rather than through 'lists' of vocabulary. There's a decent glossary at the end of the book, so that the same vocabulary is not constantly repeated throughout the book, but gradual introduction helps a lot with memorizing some basic vocabulary.
Third, graphical notations are used, which do mirror what a beginner does to help oneself analyze a text, match terms which need to be grouped, etc. If one is lazy, this can be a hindrance (as one will believe one is able to do the analysis while merely being able to follow another's analysis), but if one truly uses one's brain to decypher each example, this then constitutes a fantastic example of "leading/teaching by example".
I cannot stress enough how good these examples are! And they, too, come from the Theravada canon; with even clearer references (precise sutras) than in the previously mentioned book (who merely gives the collection a sutra is from, but not the precise sutra, and there can be hundreds of sutra in a collection…).