The shofar is generally discussed in either a practical pshat manner, focusing on the shapru maaseichem aspect of it as a call for us to return to Hashem and mend our ways, or on a deeper kabbalistic level which is generally too deep and esoteric for the average person to understand.  I would like to focus on the deeper aspects of the shofar but break it down in a way that perhaps can be more easily understood.

We find in Pirke d'R'Eliezer in the name of R' Zecharia that the ram, which Chazal teach us was created on Erev Shabbat Bein Hashmashot, desired to come close to Avraham and Yitzchak, but the angel known as s"m tried to prevent this.  The Torah describes Avraham's spotting of the ram: "caught in the thicket by its horns" (Bereishit 22:13) which then put out its legs and held on to Avraham's clothing.  Avraham saw the ram's mesirut nefesh and offered it as a korban in place of his son Yitzchak.  R' Chanina ben Dosa adds that there was nothing about this ram which was created for naught ... the skin was the belt used by Eliyahu ... the left horn was blown at Har Sinai, while the right horn is destined to be blown le-atid lavo signaling the arrival of Moshiach.

The Gemara in Rosh Hashana writes that Hashem commands us to recite psukim of malchuyot so that we may crown Him upon us, zichronot so that He will remember us for good, and with what?  With the Shofar.  R' Abahu adds that we blow with a ram's horn to remember Akeidat Yitzchak.  Just as Yitzchak was bound upon the mizbeach, so too each of us is bound upon the mizbeach when we hear the sound of the shofar, for Hashem remembers the Akeida and it becomes as if we ourselves are bound as well.

There are three physical acts associated with the shofar - there is the blowing of the air, the lips which touch the shofar, and the physical shofar itself receiving the air and producing a sound.  The air is known as hevel of the mouth, what is hevel?  It is not simply air, it is something much greater - a person is giving over his entire self, his entire essence, this is his mesirut nefesh.  What is being produced however, is not my (or the tokei-a's) air, but the sound of the shofar itself - the bracha is "lishmoa kol shofar" - although human air is producing it, we refer to the sound as coming from the shofar.  The person blowing is not of prime significance, his hevel  being greater than his limited self.

The Shem MiShmuel explains that the shofar is produced by the hevel from the depths of the heart.  The word hevel, in fact, is comprised of the same letters as the word halev (the heart).  When I speak, my hevel is affected by the five motions of the mouth which are used to create the different vowels.  Here, however, the mouth is not involved.  When I speak, it is I who am speaking.  With the shofar, there is something much greater going on - something much deeper.  There is a limit to what words can express, even though a person's thoughts have far deeper meanings which are not portrayed in words.  Whatever thoughts we may have, the fact is rabot machashavot belev ish va-atzat Hashem hee takum.

The hevel of the heart is so much more than words.  Words are clothed - I try to find the best choice of words to express myself so I can be understood.  The sound of the shofar cannot be colored by anything which will make it appear more beautiful - it is pure.  The sound of the shofar is capable of bringing down pure spirituality from above.

The shofar, in fact, is greater than tefilla - note Rosh Hashana is called a Yom Teruah, not a Yom Tefilla.  Tefilla may be straight from my heart, but it is clothed in the physical mouth which forms the words.  The hevel of the shofar is pure ruchniyut - there is no olam hazeh intertwined with it.  Chazal tell us that bracha takes effect only on that which is not visible to the eye - the sound of the shofar is such an example.

The Ritva notes that reciting the psukim of malchuyot, zichronot, and shofarot are not enough to bring down the malchut Shamayim to this world.  Speech has gashmiyut intertwined with it - we require the sound of the shofar.  This is the meaning of the Gemara we cited above, "and how - through the shofar".  As we mentioned, although we daven hard on Rosh Hashana, it is a Yom Teruah - the tefilla is secondary to the shofar.

We can then ask, if the spoken word is on a lower level, why do we not just scream loud without uttering any words?  The answer is that we need that connection to the ram of Yitzchak, to Avraham's offering that ram.  Yitzchak's pure essence was bound upon the mizbeach.

In Parshat Bereishit, the Torah writes: "all the trees of the field were not yet on the earth, and all the herbs of the field had not yet sprouted, for Hashem had not sent rain upon the earth and there was no man to work the soil" (Bereishit 2:5).   The very next pasuk states: "a mist ascended from the earth and watered the whole surface of the soil, Hashem formed the man of dust from the ground, and He blew into his nostrils the soul of life; and man became a living being."

Rashi explains that Hashem did not bring rain until there was man to appreciate its goodness, when man appreciated its value and prayed for it then the vegetation and everything grew.

One who is so full of a yearning for ahavat Hashem and feels satisfaction in his learning and davening, utters from the depth of his heart a sound of love and satisfaction.  The hevel which he produces says it all, we know exactly what he is thinking.  His entire thought goes into this sound. 

The letters comprising the word hevel represent the five books of the Torah followed by the numerical value of the remaining letters lev representing the 32 netivot chochma - paths of wisdom - corresponding to the 32 times Elokim is mentioned in maasei bereishit - 32 paths of wisdom which the Torah brings into this world.  When I sit down to learn the five books of the Torah, I am opening my heart - these are the letters of hevel, the five combined with the 32.  There is much more which can be said here - the letters lamed and bet which spell lev - heart are also the first and last letters of the Torah.  Hashem wants our heart - Rachmana liba bai.  When a community gathers together to serve Hashem they produce one hevel pihem and loads of shefa rain down from heaven.  Chazal teach us that the world stands on the hevel pihem shel tinokot shel beit rabban.

This is the mist from the earth referred to in creation  The mist can be seen, but it is certainly not air - think of what you see when you blow on a cold day.  The hevel begins as an awakening from below producing an awakening from Above.  When we left Egypt, it was an awakening from above - Hashem pulled us out.  In the final redemption, however, it will be a result of an awakening from below - our tshuva.  The tshuva and awakening from below will produce an awakening from above - this is the mist which comes from the earth and "waters the land", it begins in the ground, rises high, and then comes back down.  This alludes to the shefa which rains down from above in the merit of the sound of the shofar.

When a person blows and there is something blocking then his air will never reach the other side.  If Hashem blew into man when Adam was created, what can be blocking, does He not fill up the entire world?  Why do we not feel this Divine Spirit?  Because our sins create the blockage - it is against Hashem's will and thus blocks the true ruach chayim from descending.

The Maharal teaches us that shofar is bina as opposed to chochma - chochma is what I am able to attain while bina implies a deeper understanding.  Often my Rebbi may say something in a shiur and I may think I could have done better, why is he stating the obvious?  Such an attitude shows that I have not uncovered what he is trying to get across - I must look between the words and letters.  The Rebbi has so much wisdom and life experience which goes into what he is saying, but I may not have enough bina to uncover this.

The Arizal writes that shofar comes from the word shfoferet - a pipe with two open ends.  Something is being passed from one end to the other.  Man has two pipes - the windpipe and the esophagus through which food travels.   The esophagus represents the din for the reshaim who take that which does not belong to them. 

The Torah tells us that Chava named one of her children Kayin because kaniti ish et Hashem - I have made a kinyan with Hashem and have become His partner in the creation.  Her second son she named Hevel, yet the Torah does not provide us with a reason for having chosen this name.  Chava wished for the kaneh - Kayin - the physical shofar - to be a tool through which the hevel passes, producing incredible Kedusha.

When I blow, I am putting my entire essence behind it.  Speaking is a much lower level.  The entire year I only speak (forbidden and even holy speech). On Rosh Hashana I try to regain the level of creation when Hashem blew into Adam HaRishon, creating life.  Chava wanted the physical shofar of Kayin, the kaneh, to be a tool for producing the Hevel, but it was not.  Kayin, the midrash states, did not believe in reward and punishment and in Olam Haba.  We must speak the entire year, but we can only say and understand so much.  Through the shofar, Hashem, in His great mercy, is giving us the opportunity to employ a higher level than speech.   The shofar is from the heart - this is the bina, the deep understanding which the Maharal spoke about.  The ability to be meivin davar mitoch davar - there is nothing physical about the sound of the shofar, it is pure spirituality.

The kaneh, as we mentioned, is from the word kinyan.  A kinyan must be made between two sides - Hashem and us.  In what way are we connected?  When we blow our essence, our hevel, and produce the shofar we are connecting to Hashem.  This is why the entire world stands on the hevel pihem of the tinokot shel beit rabban.  The entire year I must speak, on Rosh Hashana Hashem has given me a Yom Teruah to sweeten the judgment of the day.  The din is represented by the broken sounds of the shvarim and teruah.  However, there is the smooth tekiah on both sides - a sound that can keep going forever - this is the hevel.  Broken sounds are din, smooth straight sounds are rachamim and chesed.    What a great gift Hashem gave us to be able to "speak" from the heart, to sound our inner essence.  May we merit a shana tova.

Some of the ideas are based on Meor VaShemesh, the Chalban's sefer on Tishrei, and Beit Shaar on Tishrei.