  Layered kagome-lattice materials with 3$d$ transition metals provide a
fertile playground for studies on geometry frustration, band topology and other
novel ordered states. A representative class of materials AV$_3$Sb$_5$ (A=K,
Rb, Cs) have been proved to possess various unconventional phases such as
superconductivity, non-trivial $\mathbb{Z}_2$ band topology, and electronic
nematicity, which are intertwined with multiple interlaced charge density waves
(CDW). However, the interplay among these novel states and their mechanisms are
still elusive. Recently, the discovery of isostructural titanium-based
single-crystals ATi$_3$Bi$_5$ (A=K, Rb, Cs), which demonstrate similar multiple
exotic states but in the absence of the concomitant intertwined CDW, has been
offering an ideal opportunity to disentangle these complex novel states in
kagome-lattice. Here, we combine the high-resolution angle-resolved
photoemission spectroscopy and first-principles calculations to systematically
investigate the low-lying electronic structure of RbTi$_3$Bi$_5$. For the first
time, we experimentally demonstrate the coexistence of flat bands and multiple
non-trivial topological states, including type-II Dirac nodal lines and
non-trivial $\mathbb{Z}_2$ topological surface states therein. Furthermore, our
findings as well provide the hint of rotation symmetry breaking in
RbTi$_3$Bi$_5$, suggesting the directionality of the electronic structure and
possibility of emerging pure electronic nematicity in this new family of kagome
compounds, which may provide important insights into the electronic nematic
phase in correlated kagome metals.
