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Summarizing briefly from the introduction to the translation and analysis by A.V. Paribok:
The ancient parts are Book 2 and parts of Book 1 -- most likely written in Punjab (North-Western India) about 0 CE. The language of the original was probably Hybrid Sanskrit.
Book 1 (the narrative introduction) was evidently expanded and elaborated at a later time, probably to make it better fit with Theravada - the late parts include: the story of monks traveling to the heavens, Nagasena's birth, his travel to Pataliputra, Buddha's prediction of Nagasena's birth, the episode of Nagasena teaching Abhidharma expanded with TOC of Theravada's Abhidharma-pitaka.
Book 2 is the MP proper, ending with "In Milindapanha the questions and answers are finished".
The next part is Book 3 (the largest), written in 1st-2nd century CE, probably still in Hybrid Sanskrit. The way it explains controversial Buddha's quotes by interpreting them either as ultimate teaching or a mere provisional guidance, can be seen as an early element of Mahayana.
Books 2 and 3 are evidently the most interesting parts of Milindapanha as far as Buddhist teaching and philosophy.
Books 4-6 were written even later, most likely in Ceylon - already in Pali language. Of them book 4 is the earliest, written as a response to the question about existence of Buddha in Book 2 Chapter 5. Book 5 is written to address the unanswered question of Book 1: why go forth as a monk if the Goal can be attained in lay life. Book 6 was written even later, imitating the style of books 4 and 5.
The content of the text in its present form has probably stabilized by 500 CE.
In Theravada, Milindapanha is considered the middle ground between the Canon and the commentaries - because the commentaries often quote MP. Although it seems clear that MP belongs to the Sthavira family of schools (as opposed to Maha-sangha) - however when analyzed critically, MP does not exactly match the teaching of any single school, clearly mismatching Theravada on many points.
For those who'd like to read MP online, the versions I find available are T. W. Rhys David's early translation circa 1890 and Bhikkhu Pesala's highly abridged and simplified version - which he himself calls "free rendering". Unfortunately Horner's translation titled "Milinda's Questions" is only available in hard copy and the cost is prohibitive. Access To Insight has excerpts from Books 2 and 3.
There is also an abridged version edited by N. K. G. Mendis which is based on Horner's translations with some borrowings from T.W. Rhys David plus editor's own translation - this is supposed to be pretty good to deserve Bhikkhu Bodhi's endors*m*nt but I'm not entirely convinced the editor was not biased to Theravada school.