This will certainly be a long answers. You see the taxes can generally be classified into two groups’ i.e.
(1) Direct and Indirect Tax.
(2) Proportional, Progressive and Regressive Tax.

Direct taxes are those kinds of tax whose incidence cannot be shifted to anyone else. Such a tax is to be borne by the tax-payer himself. The word incidence represents the burden to be borne by the tax-payer and shifting means the process of transferring the tax. An example of direct tax would be income tax. On the other hand, indirect taxes are those kinds of tax whose incidence is actually being shifted on the ultimate consumer. Thus, here we can see that the transferring process takes place from the entrepreneur right down to the ultimate consumer. An example of indirect tax would be the tax on daily commodities e.g. food, clothing etc. The kind of taxes imposed are excise tax, sales tax etc.

A proportional tax is one that is to be paid at a fixed rate i.e. to say it is a fixed rate of everyone. Thus, if the rate of taxation as income tax is 5%, then it is said to be a proportional tax i.e. no matter how much the income is, the same rate is imposed. However, a progressive tax is a kind of tax which depends upon the level of income i.e. the higher it is the more he is taxed and vice versa. As we mentioned earlier in proportional tax, the tax payer with a higher income will naturally pay more but in the case of progressive tax, he will be paying even higher amount of income tax. On the other hand, regressive tax, in fact means that with an increase the tax burden is reduced and vice versa. Such a tax is said to be cruel in the sense that the burden is felt a lot more by the poor than the rich. Generally a government would not impose such a tax but nevertheless it does happen.

Merits of Direct Tax: Here are some advantages of direct taxes.
They are Progressive: Direct taxes are said to be progressive as they lead to more or less equal distribution of wealth. The rich pay more and poor pay less.

In Accordance with Canon of Economy: In an efficient country where almost everything is advanced proper methods are organized to collect the tax. Thus, there is no wastage of resources and hence it is in accordance with canon of economy.

In Accordance with Canon of Certainty: Direct tax is fixed at a certain rate so that people should know what they are paying and for what they are paying. Thus, this avoids any signs of corruption.

In Accordance with Canon of Simplicity: Usually direct taxation is made certain as well as simple for the people to understand simply for the same reason as above. It is direct and plain and not confusing or complicated.

Productive: Direct tax is said to be productive in the sense that the tax revenue collected is mainly used by the Government in the public interest e.g. building hospitals, schools etc.

Equal Distribution of Wealth: As we mentioned in the first point that direct taxed lead to an equal distribution of wealth, they are rather automatic stabilizers. The whole society makes an equal sacrifice to promote the national interest.

Elastic: Direct tax is elastic in the sense that if there were to be an increase in the tax rate, more revenue would be collected. Thus, the actual rate is for the Government to decide.

Automatic Stabilizers: Direct tax or rather income tax is a perfect stabilizer e.g. during the boom period more people would fall in the tax bracket and otherwise some, people would be left in the tax bracket to stabilize the economy.

Demerits of Direct Tax: Of course there are some disadvantages also.
Painful: Although it promotes the national interest, such a tax is said to be painful because the feeling of parting with hard-earned money is a rather tall sacrifice.

Dishonesty Arise: As a result of bearing the thought of parting with their income some people would resort to various tactics in, avoiding paying the income tax particularly. As a result only a certain part of their income is declared or worse still, tax collectors/ officials, are bribed and thus the national interest is rather demoted.

Inconvenience: In some countries the taxing procedure is so complicated that the technical procedure has got to be improved so that it does not result in the laymen being confused. Otherwise the laymen would have to employ a: qualified personal to look into the matter. In the end the tax payer has to pay more than the Government had bargained for.

Savings and Investments are adversely affected: Entrepreneurs particularly would be reluctant to make investment as they know that the more they invest the more tax will they have to pay. Thus, their savings for investment would also be affected.

Merits of Indirect Taxation:
Imperceptible: Indirect taxation is imperceptible because we are paying indirect taxes every other day if not everyday, through the commodities that we purchase in the market, but we never feel it.

Promotes National Interest: Indirect taxation promotes national interest because practically every one participates in promoting it. Whether rich or poor, man or woman, boy or girl, almost every body is involved.

Broad Based Tax: It is a broad based tax because it is not constrained, on a particular commodity. It covers all items right down from sweets straight up to valuable items.

Tax Revenue May easily be Increased: This is particularly true in the case of inelastic products. Since the demand for them is inelastic no matter how high the price, the commodity will still be purchased e.g. cigarettes. Thus, by increasing the price level of the inelastic commodity, government revenue will go up.

Desired Level of Consumption May easily be Obtained: Such a level can easily be attained if the Government were to impose a heavy duty on products whose consumption is intended to be reduced and similarly reduce the duty on items for which the consumption level should increase.

No Tax Evasion: Tax evasion cannot take place unless one is prepared to stop consuming. This is so because indirect tax is included in the price of the commodity i.e. sales tax, excise tax etc.

Demerits of Indirect Taxation:
Against Canon of Equity: In the canon of equity or rather equality we mentioned that the persons of the state ought to contribute a certain portion of their income in tax in accordance with their abilities. Thus, the rich pay more and the poor pay less. However, in the case of indirect taxation the rate is already fixed, rich or poor have got to pay the same. Thus, an unjust situation is created e.g. on cigarettes.

Against Canon of Economy: Relatively speaking, particularly in third world countries, the expenditure incurred on tax collection is quite high. The personal equipment etc. have got to be provided by the government practically everywhere so that every area is covered. Thus, in the end not much revenue is actually collected; not to mention the ‘leakage’ which may well arise along the way.

Inflationary in Nature: Since indirect taxes are a part of price, there is a natural tendency for inflation to take place. This is due to the fact that prices of commodities are high whereas demand for them is generally low and thus surplus product lies in the market; entrepreneurs will suffer losses and stop further investments and thus inflation takes place.

Merits of Progressive Taxation:
Equality of Sacrifice: As we mentioned in the very beginning a person with a higher income pays more tax than the person with low income because marginal utility of income decreases with every increase in it (income). Thus, even though a richer may pays more and a poor man pays less, the fact remains that both parties share the same amount of burden in terms of sacrifice.

Higher Government Revenue: In proportional taxation we mentioned that there is a fixed rate of income tax (e.g.) so that the rich pay so much and the poor pay the same and thus the Government only obtains that much revenue. However, in progressive taxation higher the income, more is the tax and thus the total tax revenue collected would be increased.

Equal Distribution of Wealth: Once again there is an equal distribution of wealth. This is so because billionaires will pay more than billionaires who pay more than the common man, who pays less than these tow elite classes. Thus, there is more or less equal distribution of wealth.

Canon of Economy is retained: Although expenditure incurred on tax collecting may already be high, but in progressive taxation higher the income, higher is the tax paid, but the expenditure incurred in collecting it does not go up or down. If it does, it will not be at the same ratio.

Demerits of Progressive Taxation:
Retards Savings and Investment: Assuming that rate of progressive is very high, this discourages saving and as a result there is retardation in investment. Hence, economic development is also retarded.

Tax Evasion: Since people know that the higher their incomes the more tax they have to pay, some pay resort to tactics in avoiding payment by presenting false statements of actual income or ever turn to bribery.

Canon of Equity: Based on this canon, the marginal utility of the last rupee as tax must be equal to both classes of the society. However, such a requirement is rather impossible to achieve as the marginal utility of the last and to the poor class will always be higher than that to the high class.

Merits of Proportional Taxation:
In Accordance with Canon of Simplicity: With proportional taxation, the tax rate is fixed to all. This simplifies matters for calculation and so on. For example, the tax is fixed at 3%. Thus, all the individuals have to do is just to deduct 3% from their annual income as income tax.

Savings and Investment are partially affected: In spite of having to pay tax, entrepreneurs will not be much discouraged because they know that this is a fixed tax and thus, to increase their profits, they can increase their saving and investment, so that more goods and services are available.

In Accordance with Canon of Certainty: Just as it is simple it is also certain. Most government have devised methods in making the public aware of the amount, purpose etc. that they are paying.

Demerits of Proportional Taxation:
Against Canon of Equality of Sacrifice: This method of taxation is rather unjust. This is because at a fixed rate the burden is felt more by the lower income group whereas the higher income group, is less affected.

Loss of Government Revenue: Through proportional taxation the total revenue collected by the Government will be much less than through progressive taxation. Furthermore, after having deducted the expenditure on collecting tax the government is left with only a small amount of revenue.

Inelastic Tax: This tax is rather a rigid one and it would be a problem particularly during crisis periods and thus the government is unable to increase or even decrease the tax rate satisfactory.

Merits of Regressive Taxation:
Promotes Investment: Regressive taxation puts the burden heavily on the poor section of the economy but the high class is not really affected. Henceforth, the rich class is able to save a lot more in the banks and this enables the banks to make investment.

Demerits of Regressive Taxation:
Unequal Distribution of Wealth: This method of taxation is unjust because the poor suffer more than the rich as with an increase in income the tax rate is lowered and vice versa.

Non Productive: Such a method of taxation is not productive and does not promote national interest. It rather makes the economy suffer i.e. the poorer section of the economy suffers. Furthermore, regressive taxes cannot be implemented on valuable commodities and are usually implemented on cheap or low price commodities such as cigarettes.