added a solution to the task

src/App.tsx

@@ -1,6 +1,5 @@
-import { PeoplePage } from './components/PeoplePage';
-import { Navbar } from './components/Navbar';
-
+import { Outlet } from 'react-router-dom';
+import { Navigation as Navbar } from './components/Navigation';
 import './App.scss';
 
 export const App = () => {
@@ -10,9 +9,7 @@ export const App = () => {
 
       <div className="section">
         <div className="container">
-          <h1 className="title">Home Page</h1>
-          <h1 className="title">Page not found</h1>
-          <PeoplePage />
+          <Outlet />
         </div>
       </div>
     </div>

src/Root.tsx

@@ -0,0 +1,22 @@
+import { HashRouter, Navigate, Route, Routes } from 'react-router-dom';
+import { App } from './App';
+import { HomePage } from './components/HomePage';
+import { PeoplePage } from './components/PeoplePage';
+import { NotFoundPage } from './components/NotFoundPage';
+
+export const Root: React.FC = () => {
+  return (
+    <HashRouter>
+      <Routes>
+        <Route path="/" element={<App />}>
+          <Route index element={<HomePage />} />
+          <Route path="people" element={<PeoplePage />}>
+            <Route path=":slug?" element={<PeoplePage />} />
+          </Route>
+          <Route path="home" element={<Navigate to="/" replace />} />
+          <Route path="*" element={<NotFoundPage />} />
+        </Route>
+      </Routes>
+    </HashRouter>
+  );
+};

src/components/HomePage/HomePage.tsx

@@ -0,0 +1,3 @@
+export const HomePage: React.FC = () => {
+  return <h1 className="title">Home Page</h1>;
+};

src/components/HomePage/index.tsx

@@ -0,0 +1 @@
+export * from './HomePage';

src/components/Navigation/Navigation.tsx

@@ -0,0 +1,28 @@
+import classNames from 'classnames';
+import { NavLink } from 'react-router-dom';
+
+export const Navigation: React.FC = () => {
+  const handleLinkClass = ({ isActive }: { isActive: boolean }) =>
+    classNames('navbar-item', { 'has-background-grey-lighter': isActive });
+
+  return (
+    <nav
+      data-cy="nav"
+      className="navbar is-fixed-top has-shadow"
+      role="navigation"
+      aria-label="main navigation"
+    >
+      <div className="container">
+        <div className="navbar-brand">
+          <NavLink className={handleLinkClass} to="/">
+            Home
+          </NavLink>
+
+          <NavLink className={handleLinkClass} to="/people">
+            People
+          </NavLink>
+        </div>
+      </div>
+    </nav>
+  );
+};

src/components/Navigation/index.tsx

@@ -0,0 +1 @@
+export * from './Navigation';

src/components/NotFoundPage/NotFoundPage.tsx

@@ -0,0 +1,3 @@
+export const NotFoundPage: React.FC = () => {
+  return <h1 className="title">Page not found</h1>;
+};

src/components/NotFoundPage/index.tsx

@@ -0,0 +1 @@
+export * from './NotFoundPage';

src/components/PeopleFilters/PeopleFilters.tsx

@@ -0,0 +1,124 @@
+import React from 'react';
+import { useSearchParams } from 'react-router-dom';
+import { SearchParams } from '../../types/SearchParams';
+import { PersonSex } from '../../types/personSex';
+import { getSearchWith } from '../../utils/searchHelper';
+import classNames from 'classnames';
+import { SearchLink } from '../SearchLink';
+import { CenturyForSearch } from '../../types/CenturyForSearch';
+
+type Props = {};
+
+export const PeopleFilters: React.FC<Props> = () => {
+  const [searchParams, setSearchParams] = useSearchParams();
+
+  const query = searchParams.get(SearchParams.QUERY) || '';
+  const sex = searchParams.get(SearchParams.SEX) || PersonSex.ALL;
+  const centuries = searchParams.getAll(SearchParams.CENTURIES) || [];
+
+  const handleQuery = (event: React.ChangeEvent<HTMLInputElement>) => {
+    const params = new URLSearchParams(searchParams);
+    const newQuery = event.target.value || null;
+
+    if (newQuery) {
+      params.set(SearchParams.QUERY, newQuery);
+    } else {
+      params.delete(SearchParams.QUERY);
+    }
+
+    setSearchParams(getSearchWith(params, { query: newQuery }));
+  };
+
+  const handleCenturyOfBirth = (century: string) => {
+    return centuries.includes(century)
+      ? centuries.filter(cent => cent !== century)
+      : [...centuries, century];
+  };
+
+  return (
+    <nav className="panel">
+      <p className="panel-heading">Filters</p>
+
+      <p className="panel-tabs" data-cy="SexFilter">
+        {Object.entries(PersonSex).map(([key, value]) => (
+          <SearchLink
+            key={key}
+            className={classNames({
+              'is-active': sex === value,
+            })}
+            params={{
+              sex: value,
+            }}
+          >
+            {key}
+          </SearchLink>
+        ))}
+      </p>
+
+      <div className="panel-block">
+        <p className="control has-icons-left">
+          <input
+            data-cy="NameFilter"
+            type="search"
+            className="input"
+            placeholder="Search"
+            value={query}
+            onChange={handleQuery}
+          />
+
+          <span className="icon is-left">
+            <i className="fas fa-search" aria-hidden="true" />
+          </span>
+        </p>
+      </div>
+
+      <div className="panel-block">
+        <div className="level is-flex-grow-1 is-mobile" data-cy="CenturyFilter">
+          <div className="level-left">
+            {Object.values(CenturyForSearch).map(century => (
+              <SearchLink
+                key={century}
+                data-cy="century"
+                className={classNames('button mr-1', {
+                  'is-info': centuries.includes(century),
+                })}
+                params={{
+                  centuries: handleCenturyOfBirth(century),
+                }}
+              >
+                {century}
+              </SearchLink>
+            ))}
+          </div>
+
+          <div className="level-right ml-4">
+            <SearchLink
+              data-cy="centuryALL"
+              className={classNames('button is-success', {
+                'is-outlined': centuries.length,
+              })}
+              params={{
+                centuries: null,
+              }}
+            >
+              All
+            </SearchLink>
+          </div>
+        </div>
+      </div>
+
+      <div className="panel-block">
+        <SearchLink
+          className="button is-link is-outlined is-fullwidth"
+          params={{
+            centuries: null,
+            sex: null,
+            query: null,
+          }}
+        >
+          Reset all filters
+        </SearchLink>
+      </div>
+    </nav>
+  );
+};

src/components/PeopleFilters/index.tsx

@@ -0,0 +1 @@
+export * from './PeopleFilters';