This thesis presents studies of quantum degenerate<br />atomic gases of fermionic $^6$Li and bosonic $^7$Li. Degeneracy is<br />reached by evaporative cooling of $^7$Li in a strongly confining<br />magnetic trap. Since at low temperatures direct evaporative<br />cooling is not possible for a polarized fermionic gas, $^6$Li is<br />sympathetically cooled by thermal contact with $^7$Li. In a first<br />series of experiments both isotopes are trapped in their low-field<br />seeking higher hyperfine states. A Fermi degeneracy of<br />$T/T_F=0.25(5)$ is achieved for $10^5$ fermions. For more than<br />$\sim 300$ atoms, the $^7$Li condensate collapses, due to the<br />attractive interatomic interaction in this state. This limits the<br />degeneracy reached for both species. To overcome this limit, in a<br />second series of experiments $^7$Li and $^6$Li atoms are<br />transferred to their low field seeking lower hyperfine states,<br />where the boson-boson interaction is repulsive but weak. The<br />inter-isotope collisions are used to thermalize the mixture. A<br />$^7$Li Bose-Einstein condensate (BEC) of $10^4$ atoms immersed in<br />a Fermi sea is produced. The BEC is quasi-one-dimensional and the<br />thermal fraction can be negligible. The measured degeneracies are<br />$T/T_C=T/T_F=0.2(1)$. The temperature is measured using the<br />bosonic thermal fraction, which vanishes at the lowest<br />temperatures, limiting our measurement sensitivity. In a third<br />series of experiments, the bosons are transferred into an optical<br />trap and their internal state is changed to $|F=1,m_F=1\rangle$,<br />the lowest energy state. A Feshbach resonance is detected and used<br />to produce a BEC with tunable atomic interactions. When the<br />effective interaction between atoms is tuned to be small and<br />attractive, we observe the formation of a matter-wave bright<br />soliton. Propagation of the soliton without spreading over a<br />macroscopic distance of $1.1\,$mm is observed.