This project paper is aimed to explain observability of linear time invariant dynamicalrnsystem. We develop a linear systems theory that coincides with the existing theories forrncontinuous and discrete dynamical systems. We explore observability in terms of bothrnGramian and rank conditions and establish related realizability results.rnAn observable system is one in which the latent variables can be reconstructed fromrnthe manifest variables (in sate space system, the manifest variables are input and outputrnand the latent variable is the state). In order to reconstruct the state at any time fromrnthe input and the output, due to the property of state, it su ces to reconstruct state atrna speci c time to, then, we know it every where in the future, i.e, for all t t0. Thus, wernonly need to reconstruct x(0). We will also state necessary and su cient conditions forrnthe recostructiblity of the state x(0) or observability of the system, namely, Kalmanrnobservability test, Hautus observability test and observability test using the Gramianrnmatrix of the system.rnIn addition, if the system is not observable, i.e, if the state x(0) is not reconstructible,rnusing Kalman observability decomposition, we will identify which components of x(0)rnare reconstructible and which are not. Finally we will give a test for observability of arnbehaviour. Some examples are included to show the utility of these results.rnThe rst chapter of the paper mainly discusses basic preliminaries for the discussionrnof the main topic "Observability of linear time invariant dynamical system". In here wernwill dene several terminologies both verbally and mathematically. we will also studyrnand proof some basic theorems. The later chapter discusses observability for linear timerninvariant dynamical system. Several system properties will be developed and used inrnchecking observability of a given system and prooing system related theorems.