In The Free Dictionary you usually see definitions extracted from several sources.
Usually the first one uses a phonetic notation which is unknown to me.
What's the name of that phonetic notation system?
Apparently it's called the "American Heritage Dictionary representation" (AHD), essentially identical to the one used on Wiktionary, called the "English Phonemic Representation"(enPR). It has a Wikipedia page, which shows the AHD/enPR symbols matched up with words containing that sound, and with the equivalent IPA characters: https://en.wikipedia.org/wiki/Wikipedia:American_Heritage_Dictionary_representation
Transcription systems in English-language dictionaries are generally similar, but each one seems to have its own variant! This Wikipedia page provides comparison of several such systems with each other and with the IPA: https://en.wikipedia.org/wiki/Pronunciation_respelling_for_English
The American Heritage Dictionary's website (https://www.ahdictionary.com/word/howtouse.html) links to this pdf chart of the comparison between AHD and IPA: https://www.ahdictionary.com/application/resources/misc/pronkey.pdf