The Constitution of India guarantees the citizens of the country certain fundamental rights. Therefore, under any system of rule of law , the right to appeal for redressal of one’s grievances is generally in built.
Under the Income Tax Act, 1961 following two alternatives are available to the assessee if he is not satisfied with the order passed by the Assessing Officer;

1) Appeal: First appeal against the order of the Assessing Officer shall, except in certain cases( Refusing to grant registration u/s 12AA and approval u/s 80G ), lie with the commissioner (Appeals) u/s 246A.

2) Revision: Alternatively, if the appeal is not preferred, or if could not be filed within the time limit allowed, the assesse can apply u/s 264 to the Commissioner of Income Tax for revision of the order of the Assessing Officer. This is known as revision in favour of the assessee. The Commissioner of Income Tax can also take up suo moto the case foe revision u/s 264. In some cases, the Commissioner of Income Tax can also take up the case for revision u/s 263. This is known as revision of the order of the Assessing Officer which is erroneous and prejudicial to the interest of revenue.

The assessee is given a right of appeal by the Income tax Act where he feels aggrieved by the order of the assessing authority. However, the assessee has no inherent right of appeal unless the statute specifically provides that a particular order is appealable. There are four stages of appeal under the Income-tax Act, 1961 as shown hereunder –

Assessment Order
(passed u/s 143(3), 144, 153A, 147 etc)
↓
First Appeal Commissioner
( Filed u/s 246A electronically in form 35 within 30 days of order passed)
↓
Second Appeal Appellate Tribunal
( Filed u/s 253 in form 36 within 60 days of order passed by CIT ( appeals)
↓
Third Appeal High Court u/s 260A
↓
Final Appeal Supreme Court u/s 261

Revisions
u/s 263 and 264
Section 263: The Principal Commissioner or Commissioner may call for and examine the record of any proceeding under this Act, and if he considers that any order passed therein by the Assessing officer is erroneous in so far as it is prejudicial to the interests of the revenue, he may after giving an opportunity of being heard pass such order thereon as the circumstances of the case justify, including an order enhancing or modifying the assessment, or cancelling the assessment and directing a fresh assessment.

However, Assessee has an option to file an appeal in Income Tax Appellate Tribunal against the revision order passed by CIT u/s 263.

Section 264: The Principal Commissioner or Commissioner may, either of his own motion or on an application by the assessee for revision, call for the record of any proceeding under this act in which any such order has been passed and may make such inquiry or cause such inquiry to be made and subject to the provisions of this act, may pass such order thereon, not being an order prejudicial to the assessee, as he thinks fit.

However, In this case income tax act does not provide any remedy for filling appeal to higher income tax authority . But , assessee has an option , he can take the benefit of Constitution of India. Article 226 provides every citizen of India remedy to file WRIT petition in High Court against the order passed by income tax department.

Appeals
As already discussed in above mentioned intro, the first appeal against the order of Assessing Officer shall lie to the Commissioner (Appeals) and it can only be filed by assesse only.
An assesse or any deductor or any collector who has been aggrieved by the orders (like order passed under section 147, 144, 143(3) etc) passed by the certain income tax authorities can file its first appeal to commissioner appeals u/s 246A of the income tax, act 1961.
Form of Appeal and limitation ( section 249 and Rules 45 & 46 )
1. Form: An appeal to the commissioner ( appeals) shall be made in Form 35.
2. Manner of furnishing the appeal:
a. By furnishing the form electronically under digital signature, if the return of income is furnished under digital signature.
b. By furnishing the form electronically through electronic verification code in a case not covered under sub clause (a)
c. In case where the assessee has the option to furnish the return of income in paper form, he can exercise both options of filing form in paper form or electronically.

Time limit for filing the form [section 249(2)]
The appeal should be filed within a period of 30 days of date of service of notice of demand or order passed by the authority. Further Commissioner may admit an appeal after the expiration of the prescribed period of 30 days, if he is satisfied that the appellant had sufficient cause for not presenting it within the prescribed period.