The decree on unsupervised milk (חלב עכו״ם — שמא עירב בו חלב טמא), the conditions of the heter and supervision (the non-Jew is מרתת), the Chalav Yisrael / Chalav Stam debate, the cheese of non-Jews (גבינת עכו״ם — לא פלוג) and butter (חמאה) by custom (Shulchan Aruch, Yoreh De'ah 115 — 3 se'ifim)
חָלָב שֶׁחֲלָבוֹ עוֹבֵד כּוֹכָבִים וְאֵין יִשְׂרָאֵל רוֹאֵהוּ, אָסוּר, שֶׁמָּא עֵרֵב בּוֹ חָלָב טָמֵא. וְאִם יֵשׁ דָּבָר טָמֵא בְּעֶדְרוֹ, אֲבָל יִשְׂרָאֵל יוֹשֵׁב מִבַּחוּץ וְיָכוֹל לִרְאוֹת בַּעֲמִידָתוֹ — מֻתָּר, שֶׁהֵם מִתְיָרְאִים שֶׁמָּא יַעֲמֹד וְיִרְאֶה.
Milk milked by a non-Jew when no Jew sees him is forbidden, lest he mixed in impure milk (שמא עירב בו חלב טמא). And even if there is an impure animal in his herd, if a Jew sits outside and can see by standing up — it is permitted, for the non-Jew fears he might stand and see (שמא יעמוד ויראהו).
Shulchan Aruch, Yoreh De'ah 115:1LEVEL 01
Hebrew text of the 3 se'ifim with a fluent English translation. The decree on unsupervised milk (חלב עכו״ם), the conditions of the heter and supervision (maidservants, a child, the non-Jew is מרתת), the cheese of non-Jews (גבינת עכו״ם) and butter (חמאה) explained with modern practical cases (Chalav Yisrael / Chalav Stam).
📖 StudyLEVEL 02
In-depth pilpul: the sugya of Avoda Zara, the חקירה in the foundation of the decree (a ספק of mixing — רדב״ז / פר״ח — vs דבר שנמנה במנין like יין נסך — חתם סופר, PT sk3), the two prohibitions of the milk according to the Taz, the לא פלוג of the cheese (Taz sk10), חקירות and נפקא מינות for Chalav Stam.
📖 StudyLEVEL 03
Comparative tables (milk / cheese / butter: vessels, mixture, hechsher), golden rules, classic pitfalls (the לא פלוג of the cheese, the lenient butter, the traveler between a lenient place and a stringent one) and memorization of the 3 se'ifim.
📖 StudyLEVEL 04
The practical halacha of Chalav Stam according to the Chatam Sofer, the Radvaz / Pri Chadash, the Noda BiYehuda and the Pitchei Teshuva, then Rav Moshe Feinstein (Igrot Moshe), the Chazon Ish and the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion). Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyThe Shulchan Aruch (YD 115:1) forbids milk milked by a non-Jew when no Jew saw the milking, lest he mixed in impure milk (שמא עירב בו חלב טמא). The heter holds if a Jew sits by the herd, or if it is known there is no impure animal in the herd; and even if there is, if the non-Jew milks for a Jew sitting outside who could see by standing up (the non-Jew is מרתת — שמא יעמוד ויראהו). The Rama adds that maidservants who milk in a Jew's home, or even a child (from age 9), suffice. Forbidden milk forbids even the vessels and the cheeses, but not the butter. For practical halacha, consult your Rav.
The whole modern debate turns on a חקירה: was the decree a mere ספק of mixing impure milk — in which case, where impure milk is not available, one would be lenient (רדב״ז / פר״ח, and the end of the Rama 'בזמן הזה… מותר') — or a דבר שנמנה במנין like יין נסך, binding even without fear of mixing so long as no Jew watches (חתם סופר, PT sk3)? On this basis, some permit Chalav Stam under government supervision (official inspection = כאילו ישראל רואה, the producer is מרתת before the State, parallel to שמא יעמוד ויראהו), while others require actual Chalav Yisrael (Chazon Ish, mehadrin circles); Sephardic authorities tend to permit Chalav Stam under supervision in many cases. For practical halacha, consult your Rav.
The cheese of non-Jews (גבינת עכו״ם, YD 115:2) was forbidden by decree because it was set with the rennet from the stomach of an animal they slaughtered (עור קיבת שחיטתם = נבלה) — and the decree is לא פלוג: it applies even when the cheese is set with herbs (עשבים) or with microbial or vegetable rennet, unlike the גילוי of siman 116 which is lifted today. That is why cheese always requires a hechsher. Butter (חמאה, se'if 3), by contrast, is treated more leniently by custom: it forbids neither the vessels nor its mixture, and where there is no custom to forbid it, it is permitted — especially after cooking (the צחצוחי חלב residue boils off). For practical halacha, consult your Rav.