130 pages ; Let $p$ be an odd prime and $q$ a power of $p$. By the celebrated theorem of Khare and Wintenberger (previously Serre's conjecture), an absolutely irreducible odd $2$-dimensional Galois representation $\bar{\rho}:\operatorname{G}_{\mathbb{Q}}\rightarrow \operatorname{GL}_2(\mathbb{F}_q)$ (satisfying favorable conditions) lifts to a characteristic zero Galois representation associated to a Hecke eigencuspform. Hamblen and Ramakrishna prove the analog of (the weak form of) Serre's conjecture for residually reducible $2$-dimensional Galois representations. A higher dimensional generalization of their result is proved in chapter three. Let $\bar{\rho}:\operatorname{G}_{\mathbb{Q}}\rightarrow \operatorname{GSp}_{2n}(\mathbb{F}_q)$ be a reducible and indecomposable Galois representation which is unramified outside a finite set of primes $S$ and whose image lies in a Borel subgroup. It is shown that if $\bar{\rho}$ satisfies some additional conditions, it lifts to characteristic zero Galois representation which is geometric in the sense of Fontaine-Mazur. \par In chapter four, we examine the problem of lifting a two dimensional Galois representation $\bar{\rho}:\operatorname{G}_{\mathbb{Q},S}\rightarrow \operatorname{GL}_2(\mathbb{F}_q)$ to a cuspidal Hida Family which is isomorphic to the Iwasawa algebra $\Lambda$ via the weight-space map. This was achieved for an odd, ordinary and absolutely irreducible $\bar{\rho}$ by Ramakrishna for a suitable choice of auxiliary local deformation conditions. We show that if $\bar{\rho}$ is reducible and indecomposable, one may indeed lift $\bar{\rho}$ to a Hida family $\mathbb{T}$ such that the image of the weight space map contains a congruence class of weights in $\operatorname{Spec} \Lambda$ modulo $p^2$. This Hida family is in some sense close to $\operatorname{Spec} \Lambda$, more precisely, we show that it represents a deformation functor which is arranged to have a hull isomorphic to $\operatorname{Spec} \Lambda$ (this isomorphism is not via the weight-space ...