Perhaps the most famous Talmudic story is that of the convert who wants to learn the entire Torah while standing on one foot. For good reason Shammai threw him out of his home yet Hillel famously responded "what is hateful to you do not do to others, all the rest is commentary, go and learn." (Shabbat 31a) This is a beautiful and profound answer, much more than we generally realize. 
While Hillel's answer might be a great summary of mitzvot between man and man it ignores mitzvoth between man and G-d [1]. If I treat you as I want to be treated I will not cheat you, gossip about you, take revenge against you and will help you in need. But there seems to be little relationship between how I treat you and such mitzvoth as shabbat, kashrut, mikvah or tefilllah, not to mention prohibitions such as sha'atnez, eating blood, making a tattoo or shaving with a razor.
We think such only because we view mitzvoth between man and man and those between man and G-d as two separate realms. What Hillel is teaching is that such a division is a distortion of Judaism. Mitzvoth between man and G-d are also mitzvoth between man and man. And mitzvoth between man and man are also mitzvoth between man and G-d. G-d, Israel and Torah are one. As man is created in G-d's image that means the way we act towards our fellow man demonstrates our attitudes towards G-d. And the way we best fulfill mitzvoth between man and G-d is by our actions towards our fellow man. The notion of acting towards others as we would like them to act towards us encapsulates both what we call mitzvoth between man and man and mitzvoth between man and G-d. 
I thought of this (and I elaborate on this theme here) as I learned the Mishna (Gittin 59a) listing the various rabbinic ordinances enacted mifnei darchei shalom, in order to promote peaceful relations between people.
The first example listed is that of giving of the first aliyah to the kohen. With kohanim often few and far between such a policy minimizes, if not totally avoids, disputes over who should get that first aliyah. (Sadly many have moved the dispute from the first to subsequent aliyot so while they may not fight over the first aliyahthey have no problem fighting over shlishi or shishi). Abaye questions the need of this enactment as having a kohen go first is a biblical law based on the verse "and you shall sanctify him". Our Sages understood the verse to mean "for all things that are holy, to open first, to be the first to bless and to take a nice portion first." (Gittin 59b) Rav Yosef responds that darchei shalom is not a separate rabbinic enactment but rather is the reason the Torah commanded that we give the first honour to the kohen in the first place. To this Abaye responds that this cannot be correct as "the entire Torah is because of darchei shalom". Thus there is no need to explain that giving the first aliyah to the kohen is because of darchei shalom as such an explanation would be true of the entire Torah. Rather there must be some additional specific issue specifically relating to kohanim which the Sages were referring to. 
"The entire Torah is because of darchei shalom." This is an amazing teaching but is no chidush, novel insight. It is the simple meaning, the Gemara explains, of the verse 'Her ways are ways of pleasantness and all her pathways are peace." (Mishlei 3:17) It should come as no surprise that this verse is said (and often sung out loud) whenever the Torah is put back in the aron[2]. The verse does not say her pathways are peace but all her pathways, without exception, are those of peace. It is for this reason that Torah scholars increase peace in the world (see for example Brachot 64a). By definition the more Torah one possess the more pleasantness one must display and the greater peace one must bring. 
Just as we must view each and every of the 613 mitzvot as commentary on the imperative to act towards others as we would like them to act towards us we must view all the laws of Judaism as promoting peace. One might even say these are two ways of saying the same thing. Often this is easy, at times not, yet this is the premise which underlies the Torah. Our Sages often did the work for us - for example noting how the lulav and etrog reflect the unity of the Jewish people- but generally they left that for us. 
Let us very briefly analyze some mitzvoth which we may not have related to peace - but like all mitzvoth in the Torah contain the message of darchei shalom. While the Mishkan was ostensibly dedicated to worshipping G-d it was the place where all Jews were to gather together. And each person had to contribute - a half shekel each - to its construction and upkeep. Korbanot, sacrifices, are meant to bring us closer to man (and G-d). It is why for example a korban todah, thanksgiving offering, must be eaten in one day forcing us to share the food with others lest we violate the prohibition of having leftovers. The prohibition of wearing sha'atnez (and perhaps that of mixing of meat and milk) which fascinatingly appears in the verse immediately following the mitzva to love our neighbour as ourselves points to the necessity to appreciate differences in others. While some mixtures are to be avoided there is not one size that fits all. Not taking G-d's name in vain sensitizes us to the need to be careful with our words.
All too often we lose sight of the forest for the trees focusing on the details of the mitzvoth but neglecting the overarching purpose. "The entire Torah is for the sake of peace." [3]
[1] Rashi, sensitive to this quotes a possibility that the "chavercha, others", may actually be a reference to G-d. We must not do that which is hateful to G-d which would include all mitzvoth. 
[2] Interestingly the next verse is "eitz chaim hee" that Torah is a tree of life. For reasons that I now need to investigate the authors of the siddur reversed the order of the verses.
[3] As to why we need a special decree of darchei shalom regarding the aliyot of kohanim, such will have to wait until our next post.