The heat source-Fire [i.e., Eish], Toldos Haeish, sun [i.e. Chama], Toldos Chama, electric:
Near a fire: It is Biblically forbidden to cook food whether on or near a fire. [Thus, it is not necessary for the food to be cooked over an actual fire for one to transgress the Biblical cooking prohibition, and so long as it was cooked due to the heat of a fire, it is Biblically forbidden.]
Toldos Haeish: Furthermore, it is Biblically forbidden to cook a food even with an item that was heated by a fire [to the point of Yad Soledes] even if it is no longer attached to the fire. Thus, if one heated a pan over a fire and then removed it from the fire and placed an egg into it to fry, he transgresses the Biblical cooking prohibition. [This concept is known as Toldos Haeish, which refers to an item heated from a fire. It is this prohibition that created the cooking regulations relevant to a Keli Rishon versus Keli Sheiyni and Keli Shelishi.]
Sun [i.e., Chama]-Solar cooking: It is permitted even initially to cook a food [that does not melt] under the sun. [See Q&A regarding using a solar cooker and magnifying glass]
Toldos Chama-Item heated in sun: It is Rabbinically forbidden to cook a food in an object that was heated by the sun. [This concept is known as Toldos Chamah, which refers to an item heated from a fire.] Thus, if one heated a pan under the sun and then placed an egg into it to fry, he transgresses the Rabbinical cooking prohibition. Accordingly, one may not cook a food, such as an egg, on the hood of a hot car on Shabbos.]
Hot springs: It is Rabbinically forbidden to cook a food in a hot spring on Shabbos.
Q&A on solar cooking
May one use a magnifying glass or solar cooker/oven to cook his food?
It is initially forbidden to cook food using a magnifying glass or solar cooker due to it possibly being considered Toldos Hachamah. Nonetheless, some Poskim rule that in a case of slight illness one may be lenient to ask a gentile to cook through a magnifying glass.
Cooking on a fire that was created through the magnifying glass: Some Poskim rule it is Biblically forbidden to cook food on a fire that was created using a magnifying glass, just as is prohibited by a man-made fire. Other Poskim, however, rule it is only a Rabbinical prohibition of Toldos Haor.
Is the water that is heated in solar boilers [Dud Shemesh] considered Chama or Toldos Chama? May one place water in a solar boiler on Shabbos?
Some Poskim rule that the heating of water in the solar boilers is considered Toldos Chama and is hence Rabbinically forbidden. Others rule it is considered Chama and is hence permitted to be heated. According to all the water itself is considered Toldos Chama and is hence forbidden to cook items within it.
Q&A on Electric cooking and microwave
What form of cooking is electric heat considered [i.e., electric oven, stove top]?
Electric heat is considered like a substance that was heated through fire [i.e., Toldos Haor] and is hence Biblically forbidden to cook with on Shabbos. [Thus, it is Biblically forbidden to cook foods on Shabbos on an electric stove or oven.]
The status of a Microwave:
Some Poskim rule that the heat of a microwave is considered to be like the heat of an object heated by the sun [i.e., Toldos Hachamah] which is only Rabbinically forbidden. However, some Poskim rule it is considered like the heat of an actual fire and is Biblically forbidden. This matter contains ramifications as will be explained in their relevant areas.
The status of induction cooking:
Seemingly this would have the same status as an electric heat, which is Biblically forbidden to use for cooking.
 Admur 318:7 “Similarly, just as it is forbidden to cook with fire so too it is forbidden to cook with an item that received its heat from fire. For example [it is forbidden] to place an egg near a pot that was heated from fire or to break [an egg] on a cloth that was heated from fire, in order [for the egg] to fry a little bit. If it was fried there to the point of the food of Ben Drusaiy, he is liable for cooking just like if he had fried it [directly] on a fire.”; Michaber 318:3; Shabbos 38
 Admur 318:7 “To cook with the [heat of the] sun directly, such as to leave an egg in the sun in order to cook, or to leave water in the sun in order to heat up is allowed because doing so is not the common form of cooking [and thus is not Biblically forbidden]. [Furthermore, this is even Rabbinically permitted as the Sages] did not decree [against cooking] with the sun due to [that one may then also come to cook] with fire being that [cooking in the heat of] the sun will not be confused with cooking with fire.”; Michaber 318:3
 Admur 318:7 “Furthermore, even [cooking] with [an item that was] heated from the sun, such as [cooking] on a cloth that got hot in the sun, is forbidden due to a decree [that if this were to be allowed then] one may come [to also cook on an item that] was heated through fire, as one who witnesses [a person cooking on such a cloth] thinks that the cloth was heated with fire.”; Michaber 318:3
 The reason: It is forbidden to do so due to a decree [that if this were to be allowed then] one may come [to also cook on an item that] was heated through fire, as one who witnesses [a person cooking on such a cloth] thinks that the cloth was heated with fire. However, to cook under the sun is permitted even Rabbinically as cooking in the heat of the sun will not be confused with cooking with fire. [Admur ibid]
 Admur ibid “Thus it is forbidden to roll [the egg] on sand, and road dust which have become hot from the [rays of] the sun.”; M”A 318; M”B 318:20
 Admur 318:8 “One who cooks in the hot springs of Tiveria is exempt [from liability], because they are comparable to an item heated by the sun. Nevertheless, it is Rabbinically forbidden [to cook in it] even if the food is positioned on top of [the spring] and thus cooks from above.”
 Kaf Hachaim 318:46 [regarding making a flame with the glass]; See Maor Hashabbos 1:17 footnote 8 [p. 284]
 Shevisas Hashabbos Mivashel 44
 The reason: As perhaps this is considered Chamah, or perhaps it is considered Toldas Chamah, hence through a gentile one may be lenient in a time of illness.
 Lev Chaim 3:68
 Shaar Zekeinim 2 p. 86
 Minchas Yitzchak 4:44; Shevet Halevy 1:94; Bris Olam Ofeh 13
 Tzitz Eliezer 7:19; Yabia Omer 4:34; Har Tzevi 188; SSH”K 1:45 simply writes “It is proper…”
 See Minchas Shlomo 2:19; Piskeiy Teshuvos 277:4 footnote 28; Shabbos Kehalacha Vol. 1 p. 25; Beis Yitzchak 1:120; Pnei Meivin 56; Tzafnas Paneiach 273:3; Nishmas Shabbos 77; Levushei Mordechai 1:47; Mahrsham 2:246 [lenient]; Achiezer 3:60 [Biblical]; Eretz Tzevi 1:62; Chazon Ish 50:9; Zer Hashulchan 87:6
Other opinions: Some Poskim suggest that electric heat is only Rabbinically forbidden. [See Shabbos Kehalacha Vol. 1 p. 25 that this has been discussed amongst the Poskim and their final ruling is that it is considered like heat of a fire.]
 Background: There seems to be a dispute between Reb Moshe Feinstein and Reb Shlomo Zalman Aurbach on this subject. Reb moshe contends that regarding Shabbos a microwave is considered cooking and Reb Shlomo disagrees. The Gemara Shabbos 39a records a machlokes about cooking in the sun (bishul b’chama). Rabbi Yose maintains that one is chayav for cooking in the sun (just like cooking on a fire), while the Chachamim are of the opinion that bishul b’chama is patur. Rashi Shabbos 39a s.v d’shari explains the opinion of the Chachamim as follows: bishul b’chama is patur because it is not the normal way to cook. R’ Moshe Feinstein Vol. 3, Responsa 52 extrapolates from this Rashi that had bishul b’chama been a normal way of cooking, it would be no different from cooking on a fire. In other words, bishul min hatorah can be accomplished even without an actual fire and this is why cooking in a microwave oven is considered bishul d’oraysa (since it is normal to cook in a microwave oven). However, R’ Shlomo Zalman Shemiras Shabbos 1 note 12 argues that Rashi meant that, by definition, cooking with anything other than a real fire (such as the sun or a microwave oven) is not bishul min hatorah. [Writtn by a student in our Semicha program]
 Rav SZ”A in SSH”K 1 footnote 12; Shabbos Kehalacha Vol. 1 p. 181 and 261
 Igros Moshe 3:52