is “self-evident,” the signers assert,

that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

The document then asserts that men create government to “secure these rights,” but when government fails to do so, they have the right and even the responsibly to change it. This is not done lightly, of course, but in the case of despotism, people must throw off corrupt government and make a change for the better.

Indeed, this is exactly what the Declaration's signers believed has happened. The king of Great Britain has far overstepped the boundaries of good government. The document's next section contains a long list of grievances against the king, and these grievances serve as the reasons behind the Declaration. The king interfered with the proper procedure of law and obstructed justice. He taxed citizens without their consent. He deprived them of their liberty in numerous ways. The Americans have tried everything they could, petitioning the king again and again, but the time for petitions is now over.

In the Declaration's third section, the signers explain what they are going to do. They are declaring their independence from Great Britain and establishing their colonies as the United States. From here on, they are “Free and Independent,” and they will rule themselves in all ways. To this, they conclude,

we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.

Technically, it seems like you can divide the Declaration of Independence into four parts, assuming you're including the Preamble. The Preamble serves as an introduction to the document, announcing its purpose: it states, in reference to the cause of colonial independence, that the colonists ought to "declare the causes which impel them to separation." From here, we arrive at the document proper.

The first section of the Declaration of Independence is largely political philosophy, shaped by the ideas of John Locke. Here, the Declaration of Independence sets out a series of philosophical claims, regarding the purpose of government and its relationship with the governed. This vision is ultimately shaped by the concept of Natural Rights ("Life, Liberty, and the pursuit of Happiness"), and it states that governments are ultimately created "to secure these rights." From this point, the Revolutionaries can make a claim that their rebellion is a legitimate action: if the British government has failed to uphold that original social contract, then it has lost its claim to legitimacy and the colonies have the right to create a new government for themselves. You can consider this the theoretical architecture of the American Revolution which justifies the claim to rebellion.

The second section of the Declaration of Independence is far more evidentiary in nature and comprises of a list of accusations against King George and the British government, detailing the various ways in which the colonies have been mistreated and abused. Through providing this list of grievances, the Declaration of Independence is building a case against Britain to support the Revolution's claim as a legitimate political action.

The final section of the Declaration of Independence provides a conclusion to the document as well as the final resolution that follows from the earlier two sections. It is a statement of the colonies' intention to separate from Britain. If the earlier two sections set forth the argumentation and evidence which would favor the colonists' claim to rebellion, then this final section voices the colonists' intention to invoke said claim and set about creating their own country separate from Britain.

If you exclude the Preamble, the Declaration of Independence can be divided into three parts. The first part declares the rights of citizens and is heavily influenced by the works of the English political philosopher John Locke. This is the portion that has the famous line about "unalienable rights."

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of happiness.

The first part also asserts that if a government fails to protect these rights, the citizens have the duty to remove that government. This transitions nicely into the second part of the Declaration of Independence which outlines how the King and Parliament have not protected the rights of the colonists. Twenty-seven grievances in all are listed. An example of a grievance from the document:

He has refused for a long time, after such dissolutions, to cause others to be elected; whereby the Legislative powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within.

The third part of the document is the official declaration that grants the colonists freedom and independence from England.  This portion is the major purpose of the document in the first place and the reason Independence Day is celebrated on the day the document was signed.  

....solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved.....

The Declaration of Independence has several parts. The first part stated that when a group of people wants to be free from another group of people, the people should explain why they want to be free. This section is called the preamble.

The second part of the Declaration of Independence explained that people have rights that can’t be taken away. These rights include the right to life, liberty, and the pursuit of happiness. They are known as unalienable rights. Additionally, the job of government is to protect our rights. When government fails to protect our rights, the people must remove that government.

The third section of the Declaration of Independence, which is the largest section, is the list of complaints against the King. The colonists had many complaints about the actions of the King as well as the British government. The statement that said we were now free from British rule followed the third section.

The three most important sections of the Declaration of Independence collectively represent an argument encased in a logical, dialectical structure that culminates in a synthesis. What does this mean? Simply that the Declaration embodies a particular kind of dynamic thought process that goes through various contradictions but transcends them to arrive at a conclusion.

So the first of the three main sections is a declaration of natural rights. The signatories of the Declaration believe that they are possessed of inalienable rights, granted to them by God, and which they hold merely by virtue of being human. This could be described as the document's thesis, or mission statement, if you will. This is the theoretical basis of the Founding Fathers' demands.

Then we have an extensive list of grievances. Here, the colonists' leaders set out the various governmental and legal abuses they believe have been carried out by King George III and his administration. This section is the antithesisof the Declaration, as the actions of the British government are completely opposed to respecting the colonists' innate natural rights.

Finally, we have the resolution in which the colonists explicitly declare their independence from the mother country. The last section is a synthesis of the previous two. This means that its argument contains elements of both the thesis (that all men are possessed of natural rights) and the antithesis (that the British have violated those rights). In order to protect the natural rights with which they believe themselves endowed, the colonists will now make the final break with Britain.

The first part of the Declaration of Independence is probably the most famous and certainly the most often-quoted. It might be called a "statement of purpose," because in it Jefferson and the signers declared the reason for the document, which was to explain their justifications for declaring independence from Great Britain. However, it also included the statement of the unalienable rights of men, which included "life, liberty, and the pursuit of happiness," and a brief explanation of the social contract theory upon which the Declaration was based. Essentially, the Declaration states that the purpose of government is to preserve the fundamental rights of man, and that when governments fail to protect these rights, the people have the right to overthrow them.

The second part of the Declaration is a long list of grievances against King George. These grievances range from the King's refusal to approve beneficial laws passed by colonial legislatures  to his attempts to incite "merciless Indian savages" to attack the colonists during the preceding year. Each of these accusations was intended to show that the King violated the social contract described in the first part, and that the colonies thus had the right to declare independence.

Finally, the third part is an actual declaration of independence. The signers and the people they represented declared that all political connections between themselves and Great Britain were "dissolved," and that the colonies were now "independent states." 

The first two paragraphs of the Declaration of Independence lay out the underlying philosophy of the role of government and its duty to protect the rights of all its citizens. After an opening sentence stating that it is the obligation of every revolutionary cause to state their reasons and intentions to the world, the Declaration lays out its creed. This section is heavily influenced by the ideals of certain Enlightenment thinkers, namely, John Locke and Jean-Jacques Rousseau. This part contains what are perhaps the most famous lines of the Declaration,

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness.

If a government will not protect these rights, the Declaration goes on to state, then it should be replaced with a government that will.

The following portion of the Declaration of Independence is a long list of grievances. The Declaration lists twenty-seven different ways that the English King has acted as a tyrant. He is therefore unfit to govern a nation of free people. These grievances are intended to let England, the colonists, and the rest of the world know exactly why the colonies are rebelling. It ends by stating that they have appealed to their fellow Englishmen across the Atlantic but found no aid or sympathy from them.

The text of the Declaration of Independence ends when it asserts the right of the former Thirteen Colonies to separate from Great Britain and form an independent country. The text then mentions the basic powers of a free country, such as the ability to wage war and make alliances, and the text ends with a pledge of resolve and honor from the fifty-six delegates who signed the document.