The full text of the Birchos HaTorah can be found in the Artscroll Siddur, on page 16-17, but we have excerpted them below. You will notice that, according to our presentation here, there appear to be three distinct brachos, as follows:
‘Baruch… asher kid’shanu… la’asok b’divrei T(S)orah’ [“Blessed… Who sanctified… to engross ourselves in the words of Torah”]
‘(Ve-)ha’arev nah… (long paragraph)… Baruch Atah Hashem… Ha-melamed Torah l’amo Yisrael’
[“(and) make sweet, please… (long paragraph)… Blessed Are You, Hashem… Who teaches Torah to His nation Israel”]
‘Baruch… Asher bachar banu mikol ha’amim, ve’nasan lanu es Toraso, Baruch… Nosain HaTorah’
[“Blessed… Who chose us from among all nations, and gave us His Torah, Blessed… Giver of the Torah”]
If you look closely at the Siddur, you will see that the first two are joined into one long bracha, unlike in our presentation. This difference relates to the questionable ‘vav’ (meaning “and”) placed before the phrase ‘ha’arev nah’ (make sweet, please) in the second bracha. If the ‘vav’ is used as a connecting prefix, then there are only two brachos. If not, then the second paragraph stands alone as its own bracha, and there are three. The common custom amongst Ashkenazic Jews is to combine them with the ‘vav’.
The Mishnah Berura writes the following inspiring words in his commentary to the Birchos HaTorah (translation from the Feldheim Publishers’ edition): “A prayer should issue perpetually from the lips of a father and a mother, to entreat that their children should become Torah students, righteous and of good character. One should have intense application when he says the blessing ‘Ahava Rabah’ (‘With abundant love’ – see p. 88-9) and when he says the blessing for Torah study and says, ‘May we and our offspring…’; and likewise, when he says in the prayer ‘U’Va l’Tzion (‘A redeemer shall come’, see p. 156-7): ‘so that we will not struggle in vain nor produce for futility’” (Ed: Every single Jew, even if he has no direct offspring can have this intent when he prays, for, indeed, we are all one family, all Jewish children are ours, and we should pray for their physical and spiritual welfare!)