are hints of Jefferson's true convictions cunningly woven into his famous speech.

To take one example, Jefferson states:

Let us, then, with courage and confidence pursue our own Federal and Republican principles . . .

This seems perfectly reasonable. Jefferson gives every impression of being above the fray, adopting the disinterested standpoint of the great statesman. However, I'd like to suggest that Jefferson is doing something rather different. He is essentially giving notice to friend and foe alike that he will doggedly pursue his deeply-held republican principles come what may. Of course, Federalists are perfectly free to do likewise. In a democracy, Jefferson wouldn't expect them to do anything else. But he does expect a bitter partisan battle to continue for the foreseeable future, and he intends his side to win it.

Earlier on in the Address, Jefferson famously states that

[E]very difference of opinion is not a difference of principle.

Indeed. But some differences of opinion are more closely related to principle than others. As we saw earlier, Jefferson wanted to establish republican principles on a firm basis, effectively consigning those of the Federalists to the ash-heap of history. But he must have known that these principles needed the assistance of strongly-held opinions that would enable them to be conveyed more effectively to the people.

The Republican National Gazette newspaper heaped just as much scorn, vituperation, and slanderous invective upon their Federalist opponents as the Federalist Gazette of the United States did upon the Republicans. Republican principles would be advanced by Republican opinions. That being the case, Jefferson's too-neat separation of opinion from principle strikes one as somewhat disingenuous.

None of this is meant to suggest that Jefferson's Inaugural Address was little more than a pious sham. Jefferson was a principled politician, one strongly committed to achieving a specific vision of what he wanted the United States to be. But he was also a highly skilled political operator, determined, whatever the seemingly apolitical nature of his speech, to advance the cause of his growing Republican faction.

In that sense, the most significant points in Jefferson's Inaugural Address come not from what he said but from what he implied.

The main statement that Jefferson was trying to make in his 1801 Inaugural Address was that there were no divisions in the country--"We were both Federalists and Republicans."  This was highly important, as the rhetoric of the election of 1800 was quite toxic and many people thought that the rifts created between the Federalists and Republicans would become permanent.  Jefferson hoped to work with leaders from both parties in order to ensure that the nation would be governed according to what was best for all sides.  

The Election of 1800 was one of the key events in the early period of the United States because it demonstrated that the nation was capable of passing power peacefully from one faction to the other.  Many feared that there would be a purge of the other party but this did not come to pass.  Jefferson hoped that the two parties could put aside their differences in order to ensure that the nation stayed together.  

Jefferson wisely used his Inauguration Address to heal some of the division that was caused by his election in 1800.  He understood that the political cause of partisan rancor, as evident in his political campaign, might have place in an election, but could prove to be destructive if carried over into the realm of governance.  Some of the ideas of significance in his address come from this idea of trying to find common ground.  Jefferson used the idea of speaking to both political parties in his address in embracing that "We are both Federalists and Republicans."  Such sentiments did much to bring forth the idea that Jefferson was going to govern with a sensibility that would allow bipartisanship and a sense of cooperation to emerge.  Jefferson sought to bring people together under the hopeful belief that upholding the Constitution and the nation could prove to be unifying forces:

Let us restore to social intercourse that harmony and affection without which liberty and even life itself are but dreary things.

To this point, Jefferson continues with the idea that "political intolerance" can be just as destructive as "religious intolerance."  He concludes his address with a call to humility, suggesting that he is merely a portion of a larger configuration and that he understands this in assuming the Presidency:

I ask your indulgence for my own errors, which will never be intentional, and your support against the errors of others, who may condemn what they would not if seen in all its parts. 

Jefferson uses his Inauguration Address to emphasize that modern governance can only be effective when it seeks to include as many voices as possible.