The foundation of ביטול בששים: מין במינו / מין בשאינו מינו, the taste of a non-Jew (קפילא) and its abandonment, how to estimate the sixty, the utensil that does not become נבילה, the sixty-one for the egg, the fifty-nine for the כחל, and prohibitions that are never nullified (חמץ בפסח, יין נסך) (Shulchan Aruch, Yoreh De'ah 98 — 9 se'ifim)
אִסּוּר שֶׁנִּתְעָרֵב בְּהֶתֵּר מִין בְּשֶׁאֵינוֹ מִינוֹ, כְּגוֹן חֵלֶב שֶׁנִּתְעָרֵב בְּבָשָׂר — יִטְעֲמֶנּוּ עוֹבֵד כּוֹכָבִים; אִם אוֹמֵר שֶׁאֵין בּוֹ טַעַם, אוֹ שֶׁיֵּשׁ בּוֹ טַעַם אֶלָּא שֶׁהוּא פָּגוּם, מֻתָּר. וְאִם אֵין שָׁם עוֹבֵד כּוֹכָבִים לְטָעֳמוֹ, מְשַׁעֲרִים בְּשִׁשִּׁים.
A prohibition mixed into permitted food of a different kind, for example forbidden fat (חֵלֶב) mixed into meat: a non-Jew tastes it; if he says there is no taste, or that there is a taste but it is spoiled (פגום), it is permitted. And if there is no non-Jew to taste it, one estimates in sixty.
Shulchan Aruch, Yoreh De'ah 98:1LEVEL 01
Hebrew text of the 9 se'ifim with a fluent English translation. The foundation of ביטול בששים, מין במינו / מין בשאינו מינו, the taste of the non-Jew (קפילא), how to estimate the sixty, the utensil that does not become נבילה, the 61 for the egg and the 59 for the כחל explained with practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the Taz's yesod (sk3) — מין במינו nullified ברוב mi-deoraïta vs מין בשאינו מינו טעם כעיקר deoraïta, the ספק לקולא / לחומרא, the דעת שוטים (sk6), the מחלוקת ב״י / רמ״א on כלים נעשים נבילה (sk8), שם vs טעם, חקירות and נפקא מינות.
📖 StudyLEVEL 03
Comparative tables (מין במינו / מין בשאינו מינו, spilled, before us, 60 / 61 / 59), golden rules, classic pitfalls (ספק הבא ממיעוט הכרה, 60 against all, כלים that are not נ״נ, מצטרף לבטל) and memorization of the 9 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Shach, Taz, Pri Megadim and Pitchei Teshuva (the מחלוקת Shach / Taz of se'if 2 on the spilled שאינו מינו), then the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion) and Ashkenazi poskim. Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyIt is the master rule of all of siman 98: a prohibition mixed into permitted food is nullified when there is sixty times its amount of permitted food against it (משערים בששים). When there is no non-Jew to taste, or one no longer relies on him, one estimates in sixty in every case. The Rama (הגה) rules that all prohibitions in force today are nullified in sixty, except חמץ בפסח and יין נסך. For practical halacha, consult your Rav.
In מין במינו (prohibition and permitted food of the same kind), there is no way to judge by taste (ליכא למיקם אטעמא): by Torah law the prohibition is nullified by a majority (ברוב), and it is the Sages who required sixty (Taz sk3); therefore in case of doubt (spilled) one is lenient. In מין בשאינו מינו (different kinds, e.g. חֵלֶב in meat), the taste is perceived: this is טעם כעיקר by Torah law, and sixty are required by the Torah; therefore in case of doubt one is stringent. For practical halacha, consult your Rav.
According to the Rama (se'if 8), a prohibition that gives taste in the pot and is forbidden in itself is not nullified, even in a thousand, as long as its taste is perceived. That is why salt and spices, which are made for taste (עבידי לטעמא), if they are forbidden in themselves are not nullified in sixty. Likewise חמץ בפסח and יין נסך are not nullified in sixty (each in its place). For practical halacha, consult your Rav.