Different Types of Constitution
A constitution has been defined as a body of rules established to regulate the system of government within a state. The reason for drafting a codified constitution is usually associated with the time in which a particular State is formed or associated with a major change that has taken place at national level. For instance, Italy drew up a new constitution in 1948 and Germany did the same in 1949 following their defeat in Word War II and also to mark the destruction of their previous regimes. The United States drafted a codified constitution upon independence from Britain in 1787, and India drafted a constitution after independence from Britain, in 1950.
In Britain, the constitution remains uncodified, and Bogdanor argues that the reasons for this are both historical and conceptual. The former reflects the fact that British history has remained continuous since 1689, and there has not been an obvious break which would have called for drafting a codified constitution. As such, Britain has lacked a "constitutional moment". However, that is not to say that there have not been important historical events, which influenced the way Britain is governed. There have been many such events: The Great Reform Act 1832, the Acts of the Union with Scotland and Ireland in 1707 and 1801 respectively, and the Anglo-Irish Treaty of 1921, to name a few.  Conceptually, Bogdanor argues, the reason for not having a codified constitution in Britain is because the basis of the government is the sovereignty of Parliament; this concept seems incompatible with a codified constitution simply because a codified constitution would limit that sovereignty.
Codified, Uncodified, Flexible and Inflexible Constitutions
That difference between a codified and uncodified constitution is also reflected on the fact that what is written in the constitutional document becomes a superior law that can only be judged by a Constitutional Court. This brings us to another classification of constitutions as "flexible", such as the British constitution that can be amended with ease, and "inflexible", such as the US constitution, which contains entrenchments that make it very difficult to make constitutional changes.  In constitutions of the inflexible type, it is the constitution, not the legislature that is supreme. Arguably, codified constitutions provide mechanisms to effect constitutional changes. However, making those changes is not necessarily easy. In the Canadian Constitution of 1982, the whole of Part V of the constitutional document lays down the procedures for constitutional amendment, and as a consequence, the constitution is criticised for being at a standstill.
Monarchical and Republican Constitutions
Continuing the comparison between the British and American constitutions, a further constitutional classification is possible: monarchical and republican. In the former, the monarch is the head of state, although in Britain"s case, the powers of the monarch are limited, and the Queen reigns in accordance with the constitution. The political power lies with the Prime Minister. Accordingly, a constitutional monarchy is a limited monarchy. A republican constitution on the other hand, provides for the election of a President who is the head of state and the head of the government. 
Arguably, the modern concept of a constitution has been attributed to the American Constitution of 1787, which includes a Bill of Rights, and also to the French Declaration of Rights of 1789. Both constitutions were created as a consequence of liberation, from colonialism and the monarchy respectively, in order to promote The Republic, and they had behind them violent revolutions. No longer was a constitution a body of law, institutions and customs forming the State, but it contained the concept of republicanism: the people constituting a State.
Presidential and Parliamentary Constitutions
By the fact that a republican constitution places the power in the hands of the President, while the British constitution places the power on Parliament, it would be possible to make a further classification of a constitution as "presidential", or "parliamentary". This affects the way the government operates. In the case of the former, the President will be the head of state and the head of the executive branch of the government but not the head of the legislature and not accountable to it. Furthermore, the President is not a member of the House of Representatives or the Senate. By contrast, in a Parliamentary constitution, the head of the executive branch of the government is the Prime Minister, who will also be the head of the executive, and also a member of the legislative branch of the government and accountable to it.
Federal and Unitary Constitutions
In a federal system such as the one in the US, it can also be said that the constitution is a "federal" constitution, instead of a "unitary" one. In the former, apart from a central government, there is also government at state level, with legislative competence under the constitutional arrangements. This is the case not just in the US but also in Australia, Canada and South Africa. On the other hand, Britain has a unitary constitution and it is centrally governed. However, this point may now be challenged because due to devolution powers to Scotland, Wales and Northern Ireland, perhaps there is an incipient federal aspect to the British constitution.
Political and Legal Constitutions
A further constitutional classification is a "political" and a "legal" constitution. The former is associated with holding to account those who hold political power, because it advocates that the making of laws is the exclusive domain of Parliament, and only when Parliament legislates, does the law become legitimatised. Behind a political constitution such as the British constitution is the concept of "majoritarianism", that is, that an elected majority should make the decisions affecting the voters, rather than leaving those decisions to the courts. In contrast, a legal constitution such as the American one, empowers the courts, in particular the Constitutional Court to establish the limits of government power.
Advocates of a political constitution such as Griffith and Tomkins argue that politics is the best way to exert government control because entrusting government accountability to the judiciary is neither democratic nor effective, due to the fact that judges do not have the democratic legitimacy of an elected government. As such, a political constitution is the living representation of the politics that create it. Perhaps an important difference between a political and a legal constitution is the weight given to the latter. A political constitution is flexible and changeable while a legal constitution, such as the American Constitution, has the status of a civil religion or scripture, the constitutional document is held in high esteem and the Supreme Court has a very high status within the country as the "guardian" of the Constitution.
An example of constitutional zeal is seen in the "Tea Party", which advocates carrying a copy of the constitution at all times. Furthermore, literal constitutional interpretation by the Supreme Court has helped to perpetuate the second amendment which allocates a right "to keep and bear arms", interpreted by the more liberal as applying only to a "well regulated militia" but interpreted by the Supreme Court in District of Columbia v Heller  as allowing the citizens to keep and bear arms regardless of whether certain states had banned weapons based on public safety.
Arguably, the British political constitution based on the sovereignty of Parliament has changed through the enactment of the European Communities Act 1972 (ECA) which incorporated the European Union (EU) Treaties into the British constitution, allowing also for the primacy of EU law. A further constitutional change was the incorporation of the European Convention on Human Rights into national law by the enactment of the Human Rights Act 1998 (HRA), in order to protect fundamental rights which were not considered to be protected by common law in a sufficient manner or to have proper judicial articulation.
Critics may argue that this is a sign that the British political constitution is beginning to show tendencies towards becoming a legal constitution, and that both the ECA and the HRA have created entrenchments. However, it could also be argued that this is merely the effect of Britain being part of a global economy, and that because it remains uncodified, the British constitution remains flexible, and able to change with the times.
In conclusion, whether a constitution is codified or uncodified, flexible or inflexible, presidential or monarchical, republican or parliamentary, political or legal, the one thing they have in common is that all constitutions are unique. Parpworth states, quoting Finer, that the reason for this uniqueness is that all constitutions contain autobiographical elements, and they are therefore idiosyncratic. Furthermore, they are based on different historical contexts that have generated different preoccupations, and therefore different priorities. 
Despite that, it can be argued that there is a general level that should be upheld in every constitution regardless of how it is classified: a democratic basis, protection against the abuse of power, promotion of the separation of powers, implementation of the rule of law and a proper system of checks and balances to effect government control. Constitutional maintenance should occur through active constitutional surveillance and assessment. In that sense, a political and flexible uncodified constitution has a better chance to do so, and to develop organically according to the needs of the times. However, each constitution should be able to operate within its own core of custom, convention, case law and compromise.
Bogdanor V, The New British Constitution (Hart 2009)
Bogdanor V, "Imprisoned by a Doctrine: The Modern Defence of Parliamentary Sovereignty" (2012) 32(1) Oxford Journal of Legal Studies, 179-195
Grey T C, "The Constitution as a Scripture" (1984) 37(1) Stanford Law Review, 1
Jones B C, "Preliminary warnings on "constitutional" idolatry" (2015) Jan, Public Law, 74-92
Le Sueur A, Sunkin M, Murkens J, Public Law: Text, Cases and Materials (2nd edn, OUP 2013)
Parpworth N, Constitutional and Administrative Law (5th edn, OUP, 2008)
Stevenson S, "The Supreme Court"s Renewed Interest in Autochthonous Constitutionalism"(2015) July, Public Law, 394-402
Tomkins A, Our Republican Constitution (Hart, 2005)
Tomkins A, Public Law (1st edn, OUP 2013)
District of Columbia v Heller 554 U.S. 570 (2008)
LEGISLATION AND TREATIES
Act of the Union with Scotland 1707
Act of the Union with Ireland 1801
European Communities Act 1972
European Convention on Human Rights 1950
Great Reform Act 1832
Human Rights Act 1998
Anglo-Irish Treaty 1921
 Neil Parpworth, Constitutional and Administrative Law (5th edn, OUP, 2008) 3
 Vernon Bogdanor, The New British Constitution (Hart 2009) 8 -14
 Ibid, 12
 Ibid, 13
 Parpworth (n1) 6, 7
 Ibid, 6
 Ibid, 11
 Brian Christopher Jones, Preliminary warnings on "constitutional" idolatry (2015) Jan, Public Law, 74-92
Parpworth (n1) 8
 Andrew Le Sueur, Maurice Sunkin, Jo Murkens, Public Law: Text, Cases and Materials (2nd edn, OUP 2013) 41
 Ibid, 42
 Ibid, 44
 Adam Tomkins, Our Republican Constitution (Hart, 2005) 3
 Adam Tomkins, Public Law (1st edn, OUP 2013) 3
 T C Grey, The Constitution as a Scripture (1984) 37(1) Stanford Law Review, 1
 Jones (n9) 79
 554 U.S. 570 (2008)
 Jones (n9) 86
 Vernon Bogdanor, Imprisoned by a Doctrine: The Modern Defence of Parliamentary Sovereignty (2012) 32(1) Oxford Journal of Legal Studies, 179-195
 Scott Stevenson, The Supreme Court"s Renewed Interest in Autochthonous Constitutionalism (2015) July, Public Law, 394-402
 Ibid, 401
 Parpworth (n1) 9
 Jones (n9) 89