diff --git a/distributed/core.py b/distributed/core.py
index bee894a4db6..6dadbd5a50f 100644
--- a/distributed/core.py
+++ b/distributed/core.py
@@ -43,6 +43,7 @@
     normalize_address,
     unparse_host_port,
 )
+from distributed.comm.core import Listener
 from distributed.compatibility import PeriodicCallback
 from distributed.counter import Counter
 from distributed.diskutils import WorkDir, WorkSpace
@@ -64,6 +65,8 @@
 if TYPE_CHECKING:
     from typing_extensions import ParamSpec, Self
 
+    from distributed.counter import Digest
+
     P = ParamSpec("P")
     R = TypeVar("R")
     T = TypeVar("T")
@@ -315,12 +318,55 @@ class Server:
 
     """
 
-    default_ip = ""
-    default_port = 0
+    default_ip: ClassVar[str] = ""
+    default_port: ClassVar[int] = 0
+
+    id: str
+    blocked_handlers: list[str]
+    handlers: dict[str, Callable]
+    stream_handlers: dict[str, Callable]
+    listeners: list[Listener]
+    counters: defaultdict[str, Counter]
+    deserialize: bool
+
     local_directory: str
+
+    monitor: SystemMonitor
+    io_loop: IOLoop
+    thread_id: int
+
+    periodic_callbacks: dict[str, PeriodicCallback]
+    digests: defaultdict[Hashable, Digest] | None
+    digests_total: defaultdict[Hashable, float]
+    digests_total_since_heartbeat: defaultdict[Hashable, float]
+    digests_max: defaultdict[Hashable, float]
+
+    _last_tick: float
+    _tick_counter: int
+    _last_tick_counter: int
+    _tick_interval: float
+    _tick_interval_observed: float
+
+    _status: Status
+
+    _address: str | None
+    _listen_address: str | None
+    _host: str | None
+    _port: int | None
+
+    _comms: dict[Comm, str | None]
+
+    _ongoing_background_tasks: AsyncTaskGroup
+    _event_finished: asyncio.Event
+
+    _original_local_dir: str
+    _updated_sys_path: bool
     _workspace: WorkSpace
     _workdir: None | WorkDir
 
+    _startup_lock: asyncio.Lock
+    __startup_exc: Exception | None
+
     def __init__(
         self,
         handlers,
@@ -673,13 +719,13 @@ def stop(self) -> None:
         self.monitor.close()
         if not (stop_listeners := self._stop_listeners()).done():
             self._ongoing_background_tasks.call_soon(
-                asyncio.wait_for(stop_listeners, timeout=None)
+                asyncio.wait_for(stop_listeners, timeout=None)  # type: ignore[arg-type]
             )
         if self._workdir is not None:
             self._workdir.release()
 
     @property
-    def listener(self):
+    def listener(self) -> Listener | None:
         if self.listeners:
             return self.listeners[0]
         else:
@@ -722,6 +768,7 @@ def address(self) -> str:
             if self.listener is None:
                 raise ValueError("cannot get address of non-running Server")
             self._address = self.listener.contact_address
+            assert self._address
         return self._address
 
     @property
@@ -784,7 +831,8 @@ def _to_dict(self, *, exclude: Container[str] = ()) -> dict:
         Client.dump_cluster_state
         distributed.utils.recursive_to_dict
         """
-        info = self.identity()
+        info: dict = {}
+        info.update(self.identity())
         extra = {
             "address": self.address,
             "status": self.status.name,
@@ -816,7 +864,7 @@ async def listen(self, port_or_addr=None, allow_offload=True, **kwargs):
         )
         self.listeners.append(listener)
 
-    def handle_comm(self, comm):
+    def handle_comm(self, comm: Comm) -> NoOpAwaitable:
         """Start a background task that dispatches new communications to coroutine-handlers"""
         try:
             self._ongoing_background_tasks.call_soon(self._handle_comm, comm)
@@ -824,7 +872,7 @@ def handle_comm(self, comm):
             comm.abort()
         return NoOpAwaitable()
 
-    async def _handle_comm(self, comm):
+    async def _handle_comm(self, comm: Comm) -> None:
         """Dispatch new communications to coroutine-handlers
 
         Handlers is a dictionary mapping operation names to functions or
@@ -963,7 +1011,9 @@ async def _handle_comm(self, comm):
                         "Failed while closing connection to %r: %s", address, e
                     )
 
-    async def handle_stream(self, comm, extra=None):
+    async def handle_stream(
+        self, comm: Comm, extra: dict[str, str] | None = None
+    ) -> None:
         extra = extra or {}
         logger.info("Starting established connection to %s", comm.peer_address)
 
diff --git a/distributed/http/worker/prometheus/core.py b/distributed/http/worker/prometheus/core.py
index 23aef2d9f61..f62027cf475 100644
--- a/distributed/http/worker/prometheus/core.py
+++ b/distributed/http/worker/prometheus/core.py
@@ -170,6 +170,7 @@ def collect_crick(self) -> Iterator[Metric]:
         # The following metrics will export NaN, if the corresponding digests are None
         if not self.crick_available:
             return
+        assert self.server.digests
 
         yield GaugeMetricFamily(
             self.build_name("tick_duration_median"),
diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 93a5cbdf1a0..9262eeb90b9 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -5863,7 +5863,7 @@ def worker_send(self, worker: str, msg: dict[str, Any]) -> None:
             stream_comms[worker].send(msg)
         except (CommClosedError, AttributeError):
             self._ongoing_background_tasks.call_soon(
-                self.remove_worker,
+                self.remove_worker,  # type: ignore[arg-type]
                 address=worker,
                 stimulus_id=f"worker-send-comm-fail-{time()}",
             )
@@ -5909,7 +5909,7 @@ def send_all(self, client_msgs: Msgs, worker_msgs: Msgs) -> None:
                 pass
             except (CommClosedError, AttributeError):
                 self._ongoing_background_tasks.call_soon(
-                    self.remove_worker,
+                    self.remove_worker,  # type: ignore[arg-type]
                     address=worker,
                     stimulus_id=f"send-all-comm-fail-{time()}",
                 )
diff --git a/distributed/system_monitor.py b/distributed/system_monitor.py
index 193fcdcc725..bccce514ca7 100644
--- a/distributed/system_monitor.py
+++ b/distributed/system_monitor.py
@@ -138,7 +138,7 @@ def __init__(
 
         self.update()
 
-    def recent(self) -> dict[str, Any]:
+    def recent(self) -> dict[str, float]:
         return {k: v[-1] for k, v in self.quantities.items()}
 
     def get_process_memory(self) -> int:
@@ -224,7 +224,7 @@ def __repr__(self) -> str:
             "N/A" if WINDOWS else self.quantities["num_fds"][-1],
         )
 
-    def range_query(self, start: int) -> dict[str, list]:
+    def range_query(self, start: int) -> dict[str, list[float | None]]:
         if start >= self.count:
             return {k: [] for k in self.quantities}
 
diff --git a/distributed/worker.py b/distributed/worker.py
index 044b4fbd1a9..53688d828db 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -1050,7 +1050,7 @@ async def get_metrics(self) -> dict:
 
         self.digests_total_since_heartbeat.clear()
 
-        out = dict(
+        out: dict = dict(
             task_counts=self.state.task_counter.current_count(by_prefix=False),
             bandwidth={
                 "total": self.bandwidth,
@@ -1348,9 +1348,8 @@ async def gather(self, who_has: dict[Key, list[str]]) -> dict[Key, object]:
         else:
             return {"status": "OK"}
 
-    def get_monitor_info(
-        self, recent: bool = False, start: int = 0
-    ) -> dict[str, float]:
+    # FIXME: Improve typing
+    def get_monitor_info(self, recent: bool = False, start: int = 0) -> dict[str, Any]:
         result = dict(
             range_query=(
                 self.monitor.recent()
@@ -2457,7 +2456,7 @@ async def get_profile(
     ):
         now = time() + self.scheduler_delay
         if server:
-            history = self.io_loop.profile
+            history = self.io_loop.profile  # type: ignore[attr-defined]
         elif key is None:
             history = self.profile_history
         else: