My English textbook use “iː”, and I find some online dictionaries use “ē”. Where can I find information about this phonics system?
As @ShreevatsaR commented, the situation with transcribing pronunciations is a mess. Many different systems exist; they often use the same letters in confusingly different ways.
The most widely-used and standardised system is the International Phonetic Alphabet. This is what your textbook is presumably using when it uses /iː/ — for instance, the English word seen would be transcribed in IPA as /siːn/. The reason IPA uses /iː/ here is that in many European languages, this vowel is represented by the letter i; and then the colon represents lengthening of the vowel.
IPA isn’t perfect, for a few reasons. Although in principle it’s completely standardised, books using IPA often still have minor differences in how they use it. Also, because it’s international, it’s not designed specifically for English, so often (as in this case) its symbols don’t match up well with the letters used in English spelling (and similarly for other languages). However, IPA is pretty good, and it’s by far the nearest thing in existence to a versatile, accurate, standardised system for representing pronunciation.
To learn how the IPA works, good places to start are the Wikipedia articles on the IPA itself, IPA for English, and on IPA in your own language (so you can make comparisons with pronunciations you know well).
Many books still prefer not to use IPA, I believe because they see its unusual symbols, and its differences from English spelling, as too off-putting for some readers. As a result, they use a variety of ad hoc respelling systems, usually trying to imitate ‘standard’ English spelling to a greater or lesser extent. That’s presumably what the online dictionaries you’ve found are doing with ē (e.g. Merriam-Webster has such a system). Any dictionary using such a system should have a page somewhere explaining how their system works; a good overview of the most notable systems is available at (of course) Wikipedia.
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There are many different dictionary phonetic notations, but they mostly use the same conventions for the breve (˘) and macron (¯) accent marks.
The breve indicates a "short vowel":
The macron indicates a "long vowel":
(The traditional "short"/"long" distinction would have been more accurate prior to the Great Vowel Shift.)
Part of it is whether they're looking at it historically (diachronically, I believe, is the technical term) or from the point of view of present-day usage.
Historically, the letter I (in English, as in most other European languages) had a sound similar to "ee" (like in "machine"), or maybe a little shorter. English then underwent the Great Vowel Shift, which among other things turned the "standard" sound of this letter into "ai" (like "I" the pronoun, or as in "night"). Its place was taken by E (as in "seen").
So your English textbook uses "i:" for historical reasons, while the dictionaries are using a system where, as much as possible, the vowel sounds use variations on the primary letter that bears that sound nowadays (for example, all of the various sounds that usually are spelled with E are denoted with this letter, and distinguished using markings such as acute and grave accents, circumflex, macron, and so forth).